,transcriber's ,notes3 ,underscores before and after a word or phrase indicate italics in the original text4 ,equals signs before and after a word or phrase indicate bold in the original text4 ,the carat symbol is used to indicate a superscript4 ,small capitals have been converted to ,,block capitals4 ,antiquated spellings have been preserved4 ,typographical errors have been silently corrected but other variations in spelling and punctuation remain unaltered4 ,answers are provided at the end of the book to numbered questions1 however in the original text1 numbers #bcg to #bda were omitted for some reason4 8,,laugh ,,and ,,grow ,,fat40 ,,the ,,puzzle ,,king4 ,,amusing ,,arithmetic4 ,,book-,,keeping ,,blunders4 ,,commercial ,,comicalities4 ,,curious 8,,catches40 ,,peculiar ,,problems4 ,,perplexing ,,paradoxes4 ,,quaint ,,questions4 ,,queer ,,quibbles4 ,,school ,,stories4 ,,interesting ,,items4 ,tricks with ,figures1 ,cards1 ,draughts1 ,dice1 ,dominoes1 ,etc41 ,etc41 ,etc4 ,by ,,john ,,scott1 ,author of 8,how to ,become ,quick at ,figures10 8,doctrine of ,chance10 8,tank ,calculator10 8,cyanide ,vat ,calculator10 c41 c4 ,,instructive and ,,amusing4 ,copyright4 ,brisbane1 ,h4 ,j4 ,,diddams ,,co41 ,printers and ,publishers1 ,elizabeth ,street1 ,,mdcccxcix4 ,,preface4 ,a puzzle is not solved1 impatient sirs1 ,by peeping at its answer in a trice3 ,when ,gordius1 the ploughboy ,king of ,phrygia1 ,tied up his implements of husbandry ,in the far-famed knot1 rash ,alexander ,did not undo by cutting it in twain4 ,it is hoped that this little book may prove useful1 not only in connection with puzzles for home amusement1 but that by inducing people to consider the various difficulties met with in business and trade some at least may be led to greater success in dealing with the practical puzzles and problems of everyday life4 ,it is the special desire of the author to produce a 8sugar-coated mathematical pill10 as he feels convinced that many can more easily grasp the truth when it is put before them in a light manner than when brought forward in the usual orthodox fashion4 ,no pains have been spared to make the ,,puzzle ,,king the best of its kind yet produced1 and the author here wishes to thank his many friends who have so kindly assisted him4 ,it would be well-nigh impossible to individualize2 but especial thanks are due to ,thos4 ,finney1 ,esq41 ,m4,l4,a4 7,brisbane71 for the interest he has manifested throughout1 and the kindly help he has so often rendered the author4 ,it might afford our readers some pleasure to know that this work is entirely ,australian4 ,the printers1 artist1 and author are all colonial-born1 and the production of the former two1 at any rate1 will compare favourably with that of any others4 ,the engravings throughout have been in the hands of ,mr4 ,murray ,fraser and staff1 whose experience in this special art has tended to make the book more attractive than it otherwise would have been4 ,the author is not above receiving any suggestions or contributions in the way of peculiar puzzles or commercial comicalities1 which might enhance the value of the book4 ,intending contributors are invited to communicate to the address given below1 and can rest assured that they will be remunerated according to the merits of their communications4 ,,the ,,author4 #dd1 ,pitt ,street1 ,sydney4 ,refer to ,appendix for ,answers to numbered ,problems4 ,,reading ,,big ,,numbers4 ,wonderful ,calculations4 ,although we are accustomed to speak in the most airy fashion of millions1 billions1 c41 and 8rattle0 off at a breath strings of figures1 the fact still remains that we are unable to grasp their vastness4 ,man is finite--numbers are infinite6 ,,one ,,million ,is beyond our conception4 ,we can no more realise its immensity1 than we can the tenth part of a second4 ,it should be a pleasing fact to note that commercial calculations do not often extend beyond millions2 generally speaking1 it is in the realm of speculative calculation only1 such as probability1 astronomy1 c41 that we are brought face to face with these unthinkable magnitudes4 ,who1 for instance1 could form the slightest idea that the odds against a person tossing a coin in the air so as to bring a head #bjj times in succession are #afjfichjddbehiijbgeedaifbjibcdaafbfjebb bjbiicghbgibhcecjacge 7over ,i decillion1 c47 to #a against him8 ,suppose that all the men1 women and children on the face of the earth were to keep on tossing coins at the rate of a million a second for a million years1 the odds would still be too great for us to realise against any one person succeeding in performing the above feat1 and yet the number representing the odds would be only half as long as the one already given4 ,or1 who could understand the other equally astounding fact that ,sirius1 the ,dog-star1 is #acjdcejjjjjjjjj miles from the earth1 or even that the earth itself is #edbfjjjjjjjjjjjjjjjjjj tons in weight4 ,,what ,,is ,a ,,billion ,in ,europe and ,america1 the billion is #a1jjj1jjj1jjj--;a thousand millions--but in ,great ,britain and her ,colonies1 a billion is reckoned #a1jjj1jjj1jjj1jjj--;a million millions3 a difference which should perhaps be worth remembering in the case of francs and dollars4 ,one billion sovereigns placed side by side would extend to a distance of over #ah1jjj1jjj miles1 and make a band which would pass #gcf times round the globe1 or1 if lying side by side1 would form a golden belt around it over #bf ft4 wide2 if the sovereigns were placed on top of each other flatways1 the golden column would be more than a million miles in height4 ,supposing you could count at the rate of #bjj a minute2 then1 in one hour1 you could count #ab1jjj--;if you were not interrupted4 ,well1 #ab1jjj an hour would be #bhh1jjj a day2 and a year1 or #cfe days1 would produce #aje1abj1jjj4 ,but this would not allow you a single moment for sleep1 or for any other business whatever4 ,if ,adam at the beginning of his existence1 had begun to count1 had continued to count1 and were counting still1 he would not even now1 according to the usually supposed age of man1 have counted nearly enough4 ,to count a billion1 he would require #i1eab years1 #cdb days1 #e hours and #bj minutes1 according to the above reckoning4 ,but suppose we were to allow the poor counter twelve hours daily for rest1 eating and sleeping1 he would need #ai1jbe years1 #cai days1 #aj hours and #dj minutes to count one billion4 ,a comparison-- ,one million seconds less than #ab days billion over #ca1jjj years ,a ,,good ,,catch4 #a4--;,ask a person to write1 in figures1 eleven thousand1 eleven hundred and eleven4 ,this often proves very amusing1 few being able to write it correctly at first4 #b4--;,if the eighth of #a be #cs1 what will the fifth of a #e note be8 ,,bothersome ,,bills4 ,defter at the anvil than at the desk was a village blacksmith who held a customer responsible for a little account running3 ,to menden to broken sorspuns #d punse ,to handl to a kleffr #f ,to pointen #c iron skurrs #c ,to repairen a lanton #b ,a klapper to a bel #h ,medsen attenden a cow sick the numoraman a bad i #f ,to arf a da elpen a fillup a taken in arvist #a shillin ,to a hole da elpen a fillup a taken in arvist #b ---------- ,totle of altigether #e shillins and fippunse4 ,that the honest man's services had been requisitioned for the mending of two saucepans1 putting a new handle to an old cleaver1 sharpening three blunted iron skewers1 repairing a lantern1 and providing a bell with a clapper is clear enough2 and by resolving 8a fillup0 into 8,a4 ,phillip10 all obscurity is removed from the last two items1 but 8the numoraman a bad i0 is a nut the reader must crack for himself4 ,,one ,,from ,a ,,publican4 ,he stabled a horse for a night1 and sent it home next day with a bill debiting the owner3 ,to anos #d_/f ,to agitinonimom -_/#f --- #e_/- ,a ,,laundry ,,bill4 ,a tourist in ,tasmania1 being called upon to pay a native dame of the wash-tub 8,o,oo ,,iii10 opened his eyes and ejaculated1 8,o60 but the good woman explained that he owed her just two and ninepence1 a big ,o standing for a shilling1 a little one for sixpence1 and each ,i for a penny4 ,,the ,,dutchman',s ,,account4 ,two wax dolls #ae_/- ,one wooden do #g_/f ---- ,total #g_/f ,the two dolls were #gs #f;d each1 but one 8wouldn't do20 so1 being returned1 it was taken off the account in the above manner4 ,a carpenter in ,melbourne who did a small job in an office1 made out his bill3 ,to hanging one door and myself #ads4 ,a ,,bill ,,made ,,out ,,by ,a ,,man ,,who ,,could ,,not ,,write4 ,illustration3 ,this is an exact copy of a bill sent by a bricklayer to a gentleman for work done4 ,date1 #agih4 ,this is an exact copy of a bill sent by a bricklayer to a gentleman for work done4 ,date1 #agih4 ,the bill reads thus3 ,two men and a boy1 of a day1 #b hods of mortar1 #ajs #aj;d4 ,settled4 ,a ,,bill ,,from ,,an ,,irish ,,tailor4 ,to receipting a pair of trousers #es4 ,,quite ,,right4 ,at a large manufactory a patent pump refused to work4 ,several engineers failed to discover the cause4 ,the local plumber1 however1 succeeded1 after a few minutes1 in putting it in working order1 and sent to the company-- ,to ,mending pump #b #j ,knowing how #e #j #j ------ ,total #e #b #j ,a ,,veterinary ,,surgeon',s ,,account4 ,to curing your pony1 that died yesterday1 #a #as4 #c4 ,what is the number that the square of its half is equal to the number reversed8 ,,how ,,to ,,get ,a ,,head-,,ache4 ,illustration ,naturalists state that snakes1 when in danger1 have been known to swallow each other2 the above three snakes have just commenced to perform this operation4 ,the snakes are from the same 8hatch10 and are therefore equal in age1 length1 weight1 c4 ,they all start at scratch--that is1 commence swallowing simultaneously4 ,they are twirling round at the express rate of #cjj revolutions per minute1 during which time the circumference is decreased by #a inch4 ,we would like our readers to tell us what will be the final result8 ,heads or tails1 and how many of each8 #d4 ,a man sold two horses for #ajj each2 he lost #be per cent4 on one1 and gained #be per cent4 on the other4 ,was he 8quits02 or did he lose or gain by the transaction2 and1 if so1 how much8 ,a ,,good ,,card ,,trick4 ,the performer lays upon the table ten cards1 side by side1 face downwards4 ,anyone is then at liberty 7the performer meanwhile retiring from the room7 to shift any number of the cards 7from one to nine inclusive7 from the right hand end of the row to the left1 but retaining the order of the cards so shifted4 ,the performer1 on his return1 makes a little speech3 8,ladies and gentlemen1 you have shifted a certain number of these cards4 ,now1 ,i don't intend to ask you a single question4 ,by a simple mental calculation ,i can ascertain the number you have moved1 and by my clairvoyant faculty1 though the cards are face downwards1 ,i shall pick out one corresponding with that number4 ,let me see0 7pretends to calculate1 and presently turns up a card representing 8five074 8,you shifted five cards and ,i have turned up a five1 the exact number40 ,the cards moved are not replaced1 but the performer again retires1 and a second person is invited to move a few more from right to left4 ,again the performer on his return takes up the correct card indicating the number shifted4 ,the trick1 unlike most others1 may be repeated without fear of detection4 ,illustration ,the principle is arithmetical4 ,to begin with1 the cards are arranged1 unknown to the spectators1 in the following order3 ,ten1 nine1 eight1 seven1 six1 five1 four1 three1 two1 one4 ,such being the case1 it will be found that1 however many are shifted from right to left1 the first card of the new row will indicate their number4 ,thus1 suppose three are shifted4 ,the new order of the cards will then be3 ,three1 two1 one1 ten1 nine1 eight1 seven1 six1 five1 four4 ,so far1 the trick is easy enough1 but the method of its continuance is a trifle more complicated4 ,to tell the position of the indicating card after the second removal1 the performer privately adds the number of that last turned up 7in this case three7 to its place in the row--one4 ,that gives us four1 the card to be turned up after the next shift will be the fourth4 ,thus1 suppose six cards are now shifted1 their new order will be3 ,nine1 eight1 seven1 six1 five1 four1 three1 two1 one1 ten4 ,had five cards only been shifted1 the five would have been fourth in the row1 and so on4 ,the performer now adds six1 the number of the card1 to its place in the row1 four3 the total1 ten1 gives him the position of the indicator for the next attempt4 ,thus1 suppose four cards are next shifted1 the new order will be3 ,three1 two1 one1 ten1 nine1 eight1 seven1 six1 five1 four4 ,the next calculation1 #d and #aj1 gives us a total #ad4 ,the ten is1 in this case1 cancelled1 and the fourteen regarded as four1 which will be found to be the correct indicator for the next shifting4 ,it looks more mystifying if the performer be blindfolded1 for he can tell the position of the cards with his fingers4 ,keeping his hand on the card1 he asks1 8,will you please tell me how many cards were shifted80 ,as soon as the answer is given1 he exhibits the card1 and can continue the trick as long as he pleases4 #e4 ,find #af numbers in arithmetical progression 7common difference #b7 whose sum shall be equal to #geeb1 and arrange them in #d columns1 #d numbers in each column--or1 in other words1 arrange in a square of #af numbers that when added vertically1 horizontally1 or diagonally1 the sum of each #d numbers will amount to #ahhh4 ,,some ,,curious ,,numbers4 ,if the number #cg be multiplied by #c1 or any multiple of #c up to #bg1 the product is expressed by three similar digits4 ,thus-- #cg #c #aaa #cg #f #bbb #cg #i #ccc ,the products succeed each other in the order of the digits read downwards1 #a1 #b1 #c1 etc41 these being multiplied by #c 7their number of places7 reproduce the multiplicand of #cg4 #a #c #c #b #c #f #c #c #i ,if it be multiplied by multiples of #c1 beyond #bg1 this peculiarity is continued1 except that the extreme figures taken together represent the multiple of #c that is used as a multiplier4 ,thus-- #cg #cj #aaaj1 extreme figures1 #aj #cg #cc #abba #aa #cg #cf #accb #ab ,the number #gc 7which is #cg inverted7 multiplied by each of the numbers of arithmetical progression #c1 #f1 #i1 #ab1 #ae1 etc41 produces products terminating 7unit's place7 by one of the ten different figures1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i1 #j4 ,these figures will be found in the reverse order to that of the progression1 #gc #c produces #i1 by #f produces #h1 and #i produces #g1 and so on4 ,another number which falls under some mysterious law of series is #adb1heg1 which1 multiplied by #a1 #b1 #c1 #d1 #e1 or #f gives the same figures in the same order1 beginning differently2 but if multiplied by #g1 gives all #i's4 #adb1heg multiplied by #a #adb1heg #b #bhe1gad #c #dbh1ega #d #ega1dbh #e #gad1bhe #f #heg1adb #g #iii1iii ,multiplied by #h1 it gives #a1adb1hef1 the first figure added to the last makes the original number--#adb1heg4 ,the vulgar fraction #a_/g #adb1heg4 ,the following number1 #ebfcaeghidgcfhdbaj1 if multiplied as above1 will1 in the product1 present the same peculiarities1 as also will the number #cddhbgehfbjfhifeeagbdacgicaj4 ,the multiplication of #ihgfedcba by #de #ddddddddddde ,do4 #abcdefghi #de #eeeeeeeeje ,do4 #ihgfedcba #ed #ecccccccccd ,do4 #abcdefghi #ed #ffffffffjf ,taking the same multiplicand and multiplying by #bg 7half #ed7 the product is #bf1fff1fff1ffg1 all #f's except the extremes1 which read the original multiplier 7#bg74 ,if #gb be used as a multiplier1 a similar series of progression is produced4 #f4 ,in stables five1 can you contrive to put in horses twenty-- ,in each stable an odd horse1 and not a stable empty8 8,,three ,,threes ,,are ,,ten40 ,this little trick often puzzles many3-- ,place three matches1 coins1 or other articles on the table1 and by picking each one up and placing it back three times1 counting each time to finish with number #aj1 instead of #i4 ,pick up the first match and return it to the table saying #a2 the same with the second and third1 saying #b and #c2 repeat this counting #d2 but the fifth match must be held in the hand1 saying at the time it is picked up1 #e2 the other two are also picked up and held in hand1 making #f and #g2 the three matches are then returned to the table as #h1 #i1 and #aj4 ,if done quickly few are able to see through it4 #g4 ,a man bought a colt for a certain sum and sold him #b years afterwards for #ej #ads41 gaining thereby as much per cent4 per annum compound interest as it had cost him4 ,what was the original price8 ,do ,figures ,lie8 8,figures cannot lie10 is a very old saying4 ,nevertheless1 we can all be deceived by them4 ,perhaps one of the best instances of them leading us astray is the following3-- ,an employer engaged two young men1 ,a and ,b1 and agreed to pay them wages at the rate of #ajj per annum4 ,a enquires if there is to be a 8rise10 and is answered by the employer1 8,yes1 ,i will increase your wages #e every six months40 8,oh6 that is very small2 it's only #aj per year10 replied ,a4 8,well10 said the employer1 8,i will double it1 and give you a rise of #bj per year40 ,a accepts the situation on those terms4 ,b1 in making his choice1 prefers the #e every six months4 ,at the first glance1 it would appear that ,a's position was the better4 ,now1 let us see how much each receives up to the end of four years3-- ,a ,b #ast year #ajj #ej #ast year #bnd #abj #ee #crd #adj #fj #bnd #dth #afj #fe #gj #crd #ge #hj #dth #he ---- ---- #ebj #edj ,a spieler at a ,country ,show amused the people with the following game3--,he had #f large dice1 each of which was marked only on one face--the first with #a1 the second #b1 and so on to the sixth1 which was marked #f4 ,he held in his hand a bundle of notes1 and offered to stake #ajj to #a if1 in throwing these six dice1 the six marked faces should come up only once1 and the person attempting it to have #bj throws4 ,though the proposal of the spieler does not on the first view appear very disadvantageous to those who wagered with him1 it is certain there were a great many chances against them4 ,the six dice can come up #df1fef different ways1 only one of which would give the marked faces2 the odds1 therefore1 in doing this in one throw would be #df1fee to #a against1 but1 as the player was allowed #bj throws1 the probability of his succeeding would be-- #bj ------ #df1fef ,to play an equal game1 therefore1 the spieler should have engaged to return #bccb times the money deposited4 ,,treble ,,rule ,,of ,,three4 ,if #gj dogs with #e legs each catch #ij rabbits with #c legs each in #be minutes1 how many legs must #hj rabbits have to get away from #ej dogs with #b legs each in half an hour8 #h4 ,suppose a greyhound makes #bg springs whilst a hare makes #be1 and the springs are equal3 if the hare is #ej springs before the hound at the start1 in how many springs will the hound overtake the hare8 ,the first ,arithmetic in ,english was written by ,tonstal1 ,bishop of ,london1 and printed by ,pinson in #aeeb4 ,two persons playing dominoes #aj hours a day and making #d moves a minute could continue #aah1jjj years without exhausting all the combinations of the game4 ,a schoolmaster wrote the word 8dozen0 on the blackboard1 and asked the pupils to each write a sentence containing the word4 ,he was somewhat taken aback to find on one of the slates the following unique sentence3 8,i dozen know my lesson40 #i4 ,i have a piece of ground1 which is neither square nor round1 ,but an octagon1 and this ,i have laid out ,in a novel way1 though plain in appearance1 and retain ,three posts in each compartment2 but ,i doubt ,whether you discover how ,i apportioned it1 e'en tho' ,i inform you 'tis divided into four4 ,but1 if you solve it right1 'twill afford you much delight ,and repay you for the trouble1 ,i am sure4 ,illustration ,at an examination in arithmetic1 a little boy was asked 8what two and two made80 ,answer--8,four40 8,two and four80 ,answer--8,six40 8,two and six80 ,answer--8,half-a-crown40 #aj4 ,a certain gentleman dying left his executor the sum of #c1jjj to be disposed of in the following manner1 viz43--,to give to his son #a1jjj1 to his wife #a1jjj1 to his sister #a1jjj1 and to his sister's son #a1jjj1 to his mother's grandson #a1jjj1 to his own father and mother #a1jjj1 and to his wife's own father and mother #a1jjj--required1 the scheme of kindred4 ,,copy ,,of ,,letter ,,from ,,firm ,,to ,,commercial ,,traveller4 ,sydney1 #beth ,jan41 #ahie4 ,,mr4 ,,einstein1 ,townsville1 ,,dear ,,sir1 ,ve hav receved your letter on the #ahth mit expense agount and round list4 vat ve vants is orders1 ve haf plenty maps in ,sydney vrom vich to make up round lists also big families to make expenses4 ,mr4 ,einstein ve find in going through your expenses agount #ajs4 for pilliards please don't buy no more pilliards for us4 vat ve vants is orders1 also ve do see #cjs4 for a ,horse and ,buggy1 vere is de horse and vot haf you done mit de ,buggy the rest on your expenses agount vas nix but drinks--vy don't you suck ice4 ve sended you to day two boxes cigars1 #a costed #f_/-;and the oder #c_/f you can smoke the #f_/- box1 but gif de oders to your gustomers1 ve send you also samples of a necktie vat costed us #bh_/-;gross1 sell dem for #cj_/-;dozen if you can't get #cj_/-take #h_/f1 vat ve vants is orders4 ,the neckties is a novelty as ve hav dem in stock for seven years and ain'd sold none4 ,my brother ,louis says you should stop in ,rockhampton4 ,his cousin ,marks livs dere4 ,louis says you should sell ,marks a good bill2 dry him mit de neckties first1 and sell mostly for cash1 he is ,louis's cousin4 ,ve only giv credit to dem gustomers vat pays cash4 ,don't date any more bills ahead1 as the days are longer in the summer as in the vinter4 ,don't show ,marks any of the good sellers1 and finaly remember ,mr4 ,einstein mit us veder you do bisness or you do nothings at all vat ve vants is orders4 ,yours ,truly1 ,,shadrack ,co4 ,p4,s4--,keep the expenses down4 #aa4 ,two fathers and two sons went into a hotel to have drinks1 which amounted to one shilling4 ,they each spent the same amount4 ,how much did each pay8 #ab4 ,in a cricket match1 a side of #aa men made a certain number of runs4 ,one obtained one-eighth of the number1 each of two others one-tenth1 and each of three others one-twentieth4 ,the rest made up among them #abf 7the remainder of the score71 and four of the last scored five times as many as the others4 ,what was the whole number of runs1 and the score of each man8 ,,brains v4 ,,brawn4 ,,schoolmaster--8,what is meant by mental occupation80 ,,pupil--8,one in which we use our minds40 ,,schoolmaster--8,and a manual occupation80 ,,pupil--8,one in which we use our hands40 ,,schoolmaster--8,now1 which of these occupations is mine4 ,come1 now2 what do ,i use most in teaching you80 ,,pupil 7quickly7--8,your cane1 sir60 ,illustration ,,magic ,,addition4 ,to write the answer of an addition sum1 when only one line has been written4 #gcdfh #ebagd pair #dghbe #ficda pair #cjfeh ------ #bgcdff ,tell a person to write down a row of figures4 ,now1 this row will constitute the main body of the answer4 ,tell him to write another row beneath it2 you now write a row also1 matching his second row in pairs of #i's he writes one more row1 and you again supply another in the same manner4 ,your addition sum will now consist of five lines1 four of which are paired2 the first line1 or key line1 being the answer to the sum4 ,from the unit figure in the key line deduct the number of pairs of #i's--in this instance two--and place the remainder1 #f1 as the unit figure of the answer1 then write in order the rest of the figures in the key line1 annexing the #b to the extreme left2 this will constitute the complete answer4 ,it1 of course1 is not necessary to adhere to two pairs of #i's2 there may be three1 four1 or even more2 but the total number of lines1 including the key line1 must be odd1 and the number of pairs must be deducted from the unit figure of the key line1 and this same number be written down at the extreme left4 ,the number of figures in each line should always be the same4 ,as the location of the key line may be changed if necessary1 the artifice could not easily be detected4 ,punctuation was first used in literature in the year #aebj4 ,before that time wordsandsentenceswereputtogetherlikethis 4 #ac4 ,smith and ,brown meet a dairymaid with a pail containing milk4 ,smith maintains that it is exactly half full2 ,brown that it is not4 ,the result is a wager4 ,they have no instrument of any kind1 nor can they procure one by means of which to decide the wager2 nevertheless they manage to find out accurately1 and without assistance1 whether the pail is half-full or not4 ,how is it done8--,it should be added that the pail is true in every direction4 ,illustration ,a ,,hint ,,for ,,tailors4 8,there1 stand in that position1 please1 and look straight at that notice while ,i take your measure40 ,customer reads the notice-- 8,terms ,cash40 ,,number #i4 ,if two numbers divisible by #i be added together the sum of the figures in the amount will be either #i or a number divisible by #i4 ,example3 #ed 7#a7 #cf -- #ij ,if one number divisible by #i be subtracted from another number divisible by #i1 the remainder will be either a #i or a number divisible by #i4 ,example3 #gb 7#b7 #ah -- #ed ,if one number divisible by #i be multiplied by another number divisible by #i1 the product will be divisible by #i4 ,example3 #ed 7#c7 #bg ---- #adeh ,if one number divisible by #i be divided by another number divisible by #i1 the quotient will be divisible by #i4 ,example3 #bg7cfde 7#d7 ---- #ace ,in the above examples it is worth noting that the figures in each answer added together continually produce #i4 7#a7 #ij #i 7#b7 #ed #i 7#c7 #adeh #ah #i 7#d7 #ace #i ,also1 if these answers be multiplied by any number whatever1 a similar result will be produced4 ,example3 #ace x #h #ajhj #i ,if any row of two or more figures be reversed and subtracted from itself1 the figures composing the remainder will1 when added1 be a multiple of #i1 and if added together continually will result in #i4 ,example3 #gcfb #bfcg ---- #dgbe #ah #i ,tell a person to write a row of figures1 then to add them together1 and to subtract the total from the row first written1 then to cross out any one of the figures in the answer1 and to add the remaining figures in the answer together1 omitting the figure crossed out2 if the total be now told1 it is easy to discover the figure crossed out4 ,example3 #dcfgbef #cc #cc ------- #dcfgbbc #bg ,it should be observed that the figures of the answer to the subtraction when added together equal #bg--;a multiple of #i2 this1 of course1 is always the case4 ,now1 suppose that #g was the figure crossed out1 then the sum of the figures in the answer 7omitting #g7 would be #bj2 this number being told by the person1 it is easily seen that #g must have been crossed out1 as that figure is required to complete the multiple #bg4 ,if after the figure has been crossed out1 the remaining figures total a multiple of #i1 it is evident that either a cipher or a #i must have been the figure erased4 ,multiply the digits--omitting #h--;by any multiple of #i1 and the product will consist of that multiple1 ,example3 #abcdefgi #cf #d x #i #cf -------- #ddddddddd ,if a figure with a number of ciphers attached to it be divided by #i1 the quotient will be composed of that figure only repeated as many times as there are ciphers in the dividend2 with the same figure as the remainder4 ,example3 #i7gjjjjjj -------- #gggggg-g ,,excuses4 8,miss ,brown1--,you must stop teach my ,lizzie fisical torture4 ,she needs reading and figgers more an that4 ,if ,i want her to do jumpin ,i kin make her jump40 8,please let ,willie home at #c o'clock4 ,i take him out for a little pleasure1 to see his father's grave40 8,dear ,teecher1--,please excuse ,john for staying home--he had the meesels to oblige his father40 8,dear ,miss----1 ,please excuse my boy scratching hisself1 he's got a new flannel shirt on40 8,a country schoolmaster received from a small boy a slip of paper which was supposed to contain an excuse for the non-attendance of the boy's brother4 ,he examined the paper1 and saw thereon3 8,kepatomtogoataturing40 ,unable to understand1 the small boy explained to the master that his big brother had been 8kept at home to go taturing0--that is1 to dig potatoes4 8,tommy10 said the school teacher1 8you must get your father to give you an excuse the next time you stay away from school40 8,that's no use1 teacher4 ,dad's no good at making excuses2 mother bowls him out every time40 ,,harvesting4 #ad4 ,a and ,b engage to reap a field for #ijs4 ,a could reap it in #i days by himself2 they promised to complete it in five days2 they found1 however1 that they were obliged to call in ,c 7an inferior workman7 to assist them the last two days1 in consequence of which ,b received #cs4 #i;d4 less than he otherwise would have done4 ,in what time could ,b and ,c reap the field alone8 #ae4 ,a man has a triangular block of land1 the largest side being #acf chains1 and each of the other sides #fh chains4 ,what is the value of the grass on it1 at the rate of #b an acre8 ,a school inspector in the ,north of ,ireland was once examining a geography class1 and asked the question3 8,what is a lake80 ,he was much amused when a little fellow1 evidently a true gem of the emerald isle1 answered3 8,it's a hole in a can1 sur40 ,,canvasser--8,i've got some signs that ,i'm selling to shopkeepers all day long4 ,everybody buys 'em4 ,here's one--8,if ,you ,don't ,see ,what ,you ,want1 ,ask ,for ,it40 ,,country ,,shopkeeper--8,think ,i want to be bothered with people asking for things ,i ain't got4 ,give me one reading 8,ef ,yeh ,don't ,see ,what ,yeh ,want1 ,ask ,fer ,something ,else40 ,illustration #af4 ,the number of soldiers placed at a review is such that they could be formed into #d hollow squares1 each #d deep1 and contain #bd men in the front rank more than when formed into a solid square4 ,find the whole number4 ,in the counting-house of an ,irishman the following notice is exhibited in a conspicuous place3 8,persons having no business in this office will please get it done as soon as possible and leave40 #ag4 ,upon a piece of cardboard draw ,the three designs you see-- ,i should have said of each shape four-- ,which when cut out will be1 ,if joined correctly1 that which you ,are striving to unfold-- ,an octagon1 familiar to ,my friends both young and old4 ,illustration 8,i was induced to-day1 by the importunity of your traveller10 wrote an up-country store-keeper to a ,brisbane firm1 8to give him an order2 but1 as ,i did it merely to get rid of him in a civil manner1 and to prevent my losing any more time1 ,i must ask you to cancel the same40 ,a ,,catch ,,in ,,euchre4 #ah4 ,what card in the game of euchre is always trumps and yet never turned up8 ,this often puzzles many4 ,,religious ,,reckoning4--7,,the ,,new ,,jerusalem47 ,revelations xxi4 7#ae7--8;,and he that talked with me had a golden rule to measure the city and the gates thereof and the wall thereof2 7#af7 8,and the city lieth four square1 and the length is as large as the breadth1 and he measured the city with the reed twelve thousand furlongs4 ,the length and the breadth and the height of it are equal40 #ab1jjj furlongs #g1ibj1jjj feet1 which cubed #difgicjhhjjjjjjjjjjjj cubic feet2 half of this we will reserve for the ,throne and ,court of ,heaven1 and half the balance for streets1 c41 leaving a remainder of #abdaihbgbjjjjjjjjjjjj cubic feet4 ,divide this by #djif 7the cubic feet in a room #af feet square7 and there will be #cjcbahdcge #jjjjjj rooms4 ,suppose that the world always did and always will contain #iij1jjj1jjj inhabitants1 and that a generation lasts #cc years1 making in all #b1igj1jjj1jjj every century1 and that the world will stand #ajj1jjj years1 totalling #b1igj1jjj1jjj1jjj inhabitants2 then suppose there were #ajj worlds equal to this in number of inhabitants and duration of years1 making a total of #big1jjj1jjj1jjj1jjj persons4 ,there would then be more than #ajj rooms #af feet square for each person4 #ai4 ,a man had a certain number of 's1 which he divided among #d men4 ,to the first he gave a part1 to the second one-third of what was left after the first's share1 to the third he gave five-eighths of what was left1 and to the fourth the balance1 which equalled two-fifths of the first man's share4 ,how much money did he have1 and how much did each receive1 none receiving as much as #bj8 ,,rowing ,,against ,,time4 #bj4 ,in a time race1 one boat is rowed over the course at an average pace of #d yards per second1 another moves over the first half of the course at the rate of #c yards per second1 and over the last half at #d yards per second1 reaching the winning post #ae seconds later than the first4 ,find time taken by each4 ,,stock-,,breeding4 #ba4 ,a farmer1 being asked what number of animals he kept1 answered3 8,they're all horses but two1 all sheep but two1 and all pigs but two40 ,how many had he8 ,a ,,quibble4 #bb4 ,what is the difference between twice one hundred and five1 and twice one hundred1 and ten8 #bc4 ,the product of two numbers is six times their sum1 and the sum of their squares is #cbe4 ,what are the numbers8 ,,the ,,puzzle ,,about ,,the 8,,per ,,cents40 ,there are many persons engaged in business who often become badly mixed when they attempt to handle the subject of per centages4 ,the ascending scale is easy enough3 #e added to #bj is a gain of #be2 given any sum of figures the doubling of it is an addition of #ajj4 ,but the moment the change is a decreasing calculation the inexperienced mathematician betrays himself1 and even the expert is apt to stumble or go astray4 ,an advance from #bj to #be is an increase of #be2 but the reverse of this1 that is1 a decline from #be to #bj is a decrease of only #bj4 ,there are many persons1 otherwise intelligent1 who cannot see why the reduction of #ajj to #ej is not a decrease of #ajj1 if an advance from #ej to #ajj is an increase of #ajj4 ,the other day1 an article of merchandise which had been purchased at #aj pence a pound was resold at #cj pence a pound--an advance of #bjj4 ,whereupon1 a writer in chronicling the sale said that at the beginning of the recent depression several invoices of the same class of goods which had cost over #cj pence per pound had been finally sold at #aj pence per pound--a loss of over #bjj6 ,of course there cannot be a decrease or loss of more than #ajj1 because this wipes out the whole investment and makes the price nothing4 ,an advance from #aj to #cj is a gain of #bjj2 but a decline of #cj to #aj is a loss of only #ff4 ,a very deserving trader was ruined by his miscalculations respecting mercantile discounts4 ,the article he manufactured he at first supplied to retail dealers at a large profit of about #cj4 ,he afterwards confined his trade almost exclusively to large wholesale houses1 to whom he charged the same price1 but allowed a discount of #bj1 believing that he was still realising #aj for his own profit4 ,his trade was very extensive1 and it was not till after some years that he discovered the fact that in place of making #aj profit1 as he imagined1 by this mode of making his sales he was realising only #d4 ,to #ajj value of goods he added #cj1 and invoiced them at #acj4 ,at the end of each month1 in the settlement of accounts amounting to some thousands of pounds with individual houses1 he deducted #bj1 or #bf on each #acj1 leaving #ajd1 value of goods at prime cost1 instead of #aaj1 as he all along expected4 #bd4 ,divide #ge into two parts so that three times the greater may exceed seven times the less by #ae4 #be4 ,what number is that which1 being divided by #g and the quotient diminished by #aj1 three times the remainder shall be #bd8 ,n4,b4 8,trust men and they will trust you10 said ,emerson4 8,trust men and they will bust you10 says the business man4 #bf4 ,two years ago to ,hobart-town ,a certain number of folk came down4 ,the square root of half of them got married1 ,and then in ,hobart no longer tarried2 ,eight-ninths of all went away as well 7,this is a story sad to tell73 ,the square root of four now live here in woe6 ,how many came here two years ago8 ,illustration ,,peculiarities ,,of ,,squares4 ,the following is well worth examining3-- #bb4 equals #a plus #b plus #a equals #d #cb4 #d #b #c #i #db4 #i #b #e #af #eb4 #af #b #g #be #fb4 #be #b #i #cf #gb4 #cf #b #aa #di #hb4 #di #b #ac #fd #ib4 #fd #b #ae #ha #ajb4 #ha #b #ag #ajj #aab4 #ajj #b #ai #aba #abb4 #aba #b #ba #add #bg4 ,how many inches are there in the diagonal of a cubic foot8 and how many square inches in a superficies made by a plane through two opposite edges of the cube8 ,,father 7who has helped his son in his arithmetic at home7--8,what did the teacher remark when you showed him your sums80 ,,johnny--8,he said ,i was getting more stupid every day40 ,a 8,,catch40 #bh4 #b plus #b #d #b x #b #d ,the sum and product are alike4 ,find another number that when added to itself the sum will equal its square4 #bi4 ,a man went to market with #c baskets of oranges1 which he sold at #f;d4 per dozen2 after paying #bs4 for refreshments and his coach fare1 he had remaining #gs4 ,the contents of the first and second baskets were equal to four times the first1 and the contents of the first and half the third were together equal to the second2 if he had sold the second and third baskets at #d;d per dozen1 he would have made as much money as he had now remaining4 ,what was the coach fare8 ,illustration #cj4 ,a farmer has a triangular paddock1 the sides of which are #ijj1 #gej1 and #fjj links2 he requires to cut off #c roods and #bh perches therefrom by a straight fence parallel to its least side4 ,what distance must be taken on the largest and intermediate sides8 ,,the ,,sovereigns ,,of ,,england4 ,by the aid of the following1 the order of the kings and queens of ,england may be easily remembered3-- ,first ,william the ,norman1 then ,william1 his son2 ,henry1 ,stephen1 and ,henry1 then ,richard and ,john4 ,next ,henry the ,third1 ,edwards1 one1 two1 and three2 ,and again after ,richard three ,henrys we see4 ,two ,edwards1 third ,richard1 if rightly ,i guess1 ,two ,henrys1 sixth ,edward1 ,queens ,mary and ,bess2 ,then ,jamie the ,scot1 then ,charles1 whom they slew2 ,then followed ,cromwell1 another ,charles1 too4 ,next ,james1 called the ,second1 ascended the ,throne1 ,then ,william and ,mary together came on4 ,then ,anne1 four ,georges1 and fourth ,william past1 ,succeeded ,victoria1 the youngest and last4 #ca4 ,take from #cc the fourth1 fifth1 and tenth parts of a certain number1 and the remainder is #j4 ,what is the number8 ,a ,,walking ,,match4 #cb4 ,t bets ,d he can walk #g miles to his #f for any time or distance2 so they agree to walk a certain distance1 starting from opposite points4 ,t starts from point ,m to walk to ,n4 ,d starts from ,n and walks to ,m4 ,they both started at the same moment1 and met at a spot #aj miles nearer to ,n than ,m4 ,t arrives at ,n in #h hours1 and ,d arrives at ,m in #ab hours after meeting4 ,who wins the wager8 ,how far from ,m to ,n8 ,and find the pace at which each walked8 ,,the ,,alphabet4 ,the total number of different combinations of the #bf letters of the alphabet is #djcbiadfaabffjefceehdjjjjjj4 ,all the inhabitants on the globe could not together1 in a thousand million years1 write out all the combinations1 supposing that each wrote #dj pages daily1 each page containing #dj different combinations of the letters4 8#aj ,,into #i ,,must ,,go40 ,illustration #cc4 ,ten weary footsore travellers1 all in a woeful plight1 ,sought shelter at a wayside inn one dark and stormy night4 8,nine rooms-no more10 the landlord said1 8have ,i to offer you2 ,to each of eight a single bed1 but the ninth must serve for two40 ,a din arose2 the troubled host could only scratch his head1 ,for of those tired men no two would occupy one bed4 ,the puzzled host was soon at ease 7he was a clever man71 ,and so1 to please his guests1 devised this most ingenious plan4 ,,bobby 7just from school7--8,mamma1 ,i've got through the promisecue-us examples1 an' ,i'm into dismal fractures40 #cd4 ,find the expense of flooring a circular skating rink #cj feet in diameter at #bs4 #c;d4 per square foot1 leaving in the centre a space for a band kiosk in the shape of a regular hexagon1 each side of which measures #bd inches4 #ce4 ,gold can be hammered so thin that a grain will make #ef square inches for leaf gilding4 ,how many such leaves will make an inch thick if the weight of a cubic foot of gold is #ab cwt4 #ie lbs48 ,school ,inspector3 8,what part of speech is the word 8am08 ,smart ,cockney ,youth3 8,what8 the #8'am' what you eat1 sir1 or the 'am#8 what you is80 ,,mind-,,reading ,,with ,,cards4 ,hand the pack 7a full one7 to be shuffled by as many spectators as wish2 then propose that someone takes the pack in his hand and secretly chooses a card1 not removing it1 but noticing at what number it stands counting from the bottom2 he then returns the pack to you4 ,now you have to tell what number the card is from the top4 ,you ask any one of the spectators to choose any number between #dj and #ej1 and whatever number is chosen the card will appear at that number in the pack4 ,let us suppose the number chosen is #dh4 ,you then say that it is not necessary for you to even see the cards1 which will give you a good excuse for holding them under the table1 or behind your back4 ,now subtract the number chosen1 #dh1 from #eb1 which gives remainder #d1 count off that many cards from the top1 and place them at the bottom4 ,you next say to the gentleman who chooses the card1 that 8it is now number #dh1 according to the general desire1 would you please let us know at what number it originally stood80 ,suppose he answers #g4 ,then1 in order to save time1 you commence counting from the top at that number1 dealing off the cards one by one1 calling the first card #g1 the next #h1 and so on4 ,when you reach #dh1 it will be the card the gentleman had chosen4 ,it is not necessary to limit the choice of position to between #dj and #ej1 but it is better for two reasons4 ,first1 that the number chosen be higher than that at which the card first stood1 also the higher the number chosen1 the fewer cards are there to slip from the top to the bottom4 #cf4 ,divide a ,st4 ,george cross1 by two straight cuts1 into four pieces1 so that the pieces1 when put together1 will form a square4 ,illustration ,,parsing4 8,what part of speech is #8kiss'80 asked the ,high ,school teacher4 8,a conjunction10 replied one of the smart girls4 8,wrong10 said the teacher1 severely4 8,next girl40 8,a noun10 put in a demure maiden4 8,what kind of a noun80 continued the teacher4 8,well--er--it is both common and proper10 answered the shy girl1 and she was promoted to the head of the class4 8,,quick40 ,,teacher 7to class7--8,what is velocity80 ,,bright ,,youth--8,velocity is what a person puts a hot plate down with40 ,,office ,,rules4 ,i4 ,gentlemen entering this ,office will please leave the door wide open4 ,,ii4 ,those having no business will please call often1 remain as long as possible1 take a chair1 make themselves comfortable1 and gossip with the ,clerks4 ,,iii4 ,gentlemen are requested to smoke1 and expectorate on the floor1 especially during ,office ,hours2 ,cigars and ,newspapers supplied4 ,,iv4 ,the ,money in this ,office is not intended for business purposes--by no means--it is solely to lend4 ,please note this4 ,v4 ,a ,supply of ,cash is always provided to ,cash ,cheques for all comers1 and relieve ,bank ,clerks of their legitimate duties4 ,stamped cheque forms given gratis4 ,,vi4 ,talk loud and whistle1 especially when we are engaged2 if this has not the desired effect1 sing4 ,,vii4 ,the ,clerks receive visits from their friends and their relatives2 please don't interrupt them with business matters when so engaged4 ,,viii4 ,gentlemen will please examine our letters1 and jot down the ,names and ,addresses of our ,customers1 particularly if they are in the same profession4 ,,ix4 ,as we are always glad to see old friends1 it will be particularly refreshing to receive visits and renewal of orders from any former ,customer who has passed through the ,bankruptcy ,court1 and paid us not more than ,sixpence in the ,pound4 ,a ,,warm welcome may be relied on4 ,x4 ,having no occupation for our ,office ,boy1 he is entirely at the service of callers4 ,,xi4 ,our ,telephone is always at the disposal of anyone desirous of using it4 ,,xii4 ,the following are kept at this ,office for ,public ,convenience3-- ,a ,stock of ,umbrellas 7silk71 all the ,local ,newspapers1 ,railway ,time ,tables1 and other ,guides and ,directories2 also a supply of ,note ,paper1 ,envelopes1 and ,stamps4 ,,xiii4 ,should you find our principals engaged1 do not hesitate to interrupt them4 ,no business can possibly be of greater importance than yours4 ,,xiv4 ,if you have the opportunity of overhearing any conversation1 do not hesitate to listen4 ,you may gain information which may be useful in the event of disputes arising4 ,,xv4 ,in case you wish to inspect our premises1 kindly do so during wet weather1 and carry your umbrella with you4 ,we admire the effect on the floor2 it gives an air of comfort to the establishment4 7,the ,umbrella ,stand is only for ornament1 and on no account to be used74 ,p4,s4--,our hours for listening to ,commercial ,travellers1 ,beggars1 ,hawkers1 and ,advertising ,men are all day4 ,we attend to our ,business at ,night only4 ,a ,,new ,,way ,,of ,,putting ,,it4 8,dirty days hath ,september1 ,april1 ,june and ,november2 ,from ,january up to ,may1 ,the rain it raineth every day4 ,all the rest have thirty-one1 ,without a blessed gleam of sun2 ,and if any of them had two and thirty1 ,they'd be just as wet and twice as dirty40 ,does the top of a carriage wheel move faster than the bottom8 ,this question seems absurd4 ,that the top moves faster1 however1 is perfectly correct2 for if not it would simply move round in the same place3 in a wheel on a fixed axle the bottom moves backward as fast as the top moves forward2 but in a wheel that is going forward1 drawn by a progressive axle1 the bottom does not go back at all1 but remains almost stationary until it is its turn to rise and go forward4 #cg4 ,a ,general1 arranging his army in a solid square1 finds he has #bhd men to spare1 but on increasing the sides of the square by one man1 he wants #be men to complete the square4 ,how many men has he8 8,,stewing40 #ch4 ,a student reads two lines more of 8,virgil0 each day than he did the day before1 and finds that1 having read a certain quantity in #ah days1 he will read at this rate the same quantity in the next #ad days4 ,how much will he read in the whole time8 #ci4 ,two bootmakers who lived in the town of ,b41 thrown out of employment1 resolved to go to ,g41 a town #bd miles north from ,b41 where there is a large factory2 one of them went straight on to ,g41 but the other went first to ,c41 a small township west of ,b41 and then went direct to ,g41 his whole journey being #de miles4 ,what is the distance from ,c4 to ,g48 #dj4 ,a tree which grows each year #a inch less than the previous year1 grew a yard in the first year2 the value of the tree at any time is equal to the number of pence in the cube of the number of yards of its height4 ,what is the value of the tree when done growing8 ,,this ,,often 8,,sticks0 ,,people ,,up4 #da4 ,what two odd numbers multiplied together make #g8 ,,magic ,,squares4 ,a ,magic ,square is a series of figures arranged in the equal divisions of a square in such a manner that the figures in each row when added up1 whether horizontally1 vertically1 or diagonally1 form exactly the same sum4 ,they have been called 8,magic0 because the ancients ascribed to them great virtues1 and because this arrangement of numbers formed the basis and principle of their talismans4 ,archimedes devoted a great amount of attention to them1 which has caused a great many to speak of them as 8the squares of ,archimedes40 ,they may be either odd or even4 ,when the former1 the following method will be found valuable3-- ,with the digits from #a to #be form a square so that the numbers when added up horizontally1 vertically1 or diagonally will amount to #fe4 ,method4--,imagine an exterior line of squares above the magic square you wish to form1 and another on the right hand of it4 ,these two imaginary lines are shown in the diagram4 #ah #be #b #i -------------------- #ag #bd #a #h #ae #ag -------------------- #bc #e #g #ad #af #bc -------------------- #d #f #ac #bj #bb #d -------------------- #aj #ab #ai #ba #c #aj -------------------- #aa #ah #be #b #i -------------------- #ast4 ,in placing the numbers in the square1 we must go in the ascending diagonal direction from left to right1 any number which1 by pursuing this direction1 would fall into the exterior line must be carried along that line of squares1 whether vertical or horizontal1 to the last square4 ,thus1 #a having been placed in the centre of the top row1 #b would fall into the exterior square above the fourth vertical line2 then ascending diagonally #c falls into the square diagonally from #b1 but #d falls out of it to the end of a horizontal line1 and it must be carried along that line to the extreme left and there placed4 ,resuming our diagonal ascension to the right we place #e where the reader sees it1 and would place #f in the middle of the top row1 but as we find #a is already there we look for the direction to #bnd4 ,that when in ascending diagonally we come to a square already occupied1 we must place the number which1 according to the #ast rule should go into that occupied square directly under the last number placed3 thus1 in ascending with #d1 #e1 #f1 the #f must be placed under the #e1 because the square next to #e in diagonal direction is occupied4 ,a ,promising ,sign--,i ,o ,u4 ,,how ,,to ,,find ,,the ,,total ,,of ,a ,,row ,,of ,,figures ,,in ,a ,,magic ,,square4 ,rule4--,multiply half the sum of the extremes by the square root of the greatest extreme4 ,referring to the example given above1 we see that the extremes #a and #be added equal #bf--;half of which is #ac2 this multiplied by #e 7the square root of #be7 gives #fe as the total for each row4 ,again1 in the next question1 the two extremes #a and #ha equal #hb1 half of this sum is #da1 which multiplied by #i 7the square root of #ha7 gives #cfi as the total for each row4 #db4 ,arrange the figures from #a to #ha in a square that when added up horizontally1 vertically1 or diagonally the sum will be #cfi4 ,,how ,,they ,,worked ,,it4 ,mick and ,pat1 working in the country some distance from a hotel1 arranged with the landlord to take to their hut a small keg of rum4 ,they were unable to pay for the liquor at the time1 having only one threepenny piece between them2 but ,mick proposed that every time he had a drink he would give ,pat threepence1 and ,pat also agreed to pay ,mick for his drinks1 the cash thus gathered to be brought to the publican when the keg was empty4 ,this proposal was accepted by the publican1 the keg of rum handed over to the two ,irishmen1 who immediately started on their journey4 ,they had not proceeded very far before their burden made them thirsty4 ,mick is the first to pull up with3 8,hold on1 ,pat1 ,i think ,i'll have a drink40 8,begorra10 replied ,pat1 8you'll have to pay me for it then40 ,mick hands the #c;d4 to ,pat before having a good 8pull40 ,pat now being the possessor of the price of a drink1 slakes his thirst by paying ,mick #c;d4 for it4 ,this form of payment is kept up till the rum has disappeared4 ,on their next visit to the hotel1 the #c;d piece is handed to the landlord as being payment1 according to terms of agreement adopted by him4 #dc4 ,arrange the figure's from #a to #i in a square1 so that they will add up to #ae1 horizontally1 vertically1 or diagonally4 #dd4 ,illustration3 ,n4,b4--,note this3 ,illustration #de4 ,a man sold a horse for #ce and half as much as he gave for it1 and gained thereby #aj guineas4 ,what did he pay for the horse8 ,,the ,,dishonest ,,servant4 #df4 ,a gentleman having bought #bh bottles of wine1 and suspecting his servant of tampering with the contents of the wine cellar1 caused these bottles to be arranged in a bin in such a way as to count #i bottles on each side4 ,nothwithstanding this precaution1 the servant in two successive visits stole #h bottles--#d each time--re-arranging the bottles each time so that they still counted #i on a side4 ,how did he do it8 ------------- #b #e #b #e #e #b #e #b ------------- ,,father--8,you are very backward in your arithmetic4 ,when ,i was your age ,i was doing cube roots40 ,,boy--8,what's them80 ,,father--8,what6 ,you don't know what they are8 ,my6 my6 that's terrible6 ,there1 give me your pencil4 ,now1 we take1 say1 #bhgfdbhi1 and find the cube root4 ,first1 you divide--no1 you point off--no--let me see8--um--yes--no--don't stand there grinning like a ,cheshire cat2 go upstairs and stay in your bedroom for an hour40 ,a 8,,take-,,down0 ,,with ,,cards4 ,this is a card trick which depends upon a certain 8key10 the possessor of which will always have the advantage over his uninstructed adversary4 ,it is played with the first six of each suit--the four aces in one row1 next row the deuces1 threes1 fours1 fives and sixes4 ,the object now will be to turn down cards alternately1 and endeavour to make thirty-one points by so turning without over-running that number4 ,the chief point is to count so as to end with the following numbers3 #c1 #aj1 #ag or #bd4 ,for instance1 we will suppose it your privilege to commence the count2 you would commence with #c1 and your adversary would add #f1 which would make #i2 it would be then your policy to add #a and make #aj2 then1 no matter what number he adds he cannot prevent you making #ag1 which gives you the command of the trick4 ,we will suppose he adds #f and make #af2 then you add #a and make #ag2 then he to add #f and make #bc1 you add #a and make #bd2 then he cannot add any number to make #ca1 as the highest number he can add is #f1 which would only count #cj1 so that you can easily add the remaining #a and make #ca4 ,if your adversary is not wary1 you may safely turn indifferent numbers at the beginning1 trusting to his ignorance to let you count #ag or #bd2 but1 as his knowledge increases1 he will soon learn that #bd is a critical number1 and to play for it accordingly4 ,if both players know the trick1 the first to play must be the winner1 as he is sure to begin with a #c1 which commands the game4 ,,on ,,an ,,office ,,door ,,in ,,goulburn4 ,a baptism in ,hades' depths1 ,as hot as boiling tar1 ,awaits the man who quits this room ,and leaves the door ajar4 ,but he who softly shuts the door ,shall dwell among the blest-- ,where the wicked cease from troubling ,and the weary are at rest4 #dg4 ,there are #e eggs on a dish2 divide them amongst #e persons so that each will get #a egg and yet #a still remain on the dish4 #dh4 ,if a goose weighs #aj lbs4 and a half of its own weight1 what is the weight of the goose8 ,,the ,,geometrical ,,wonder ,,and ,,arithmetical ,,absurdity4 ,take a piece of cardboard #ac inches long and #e wide1 thus giving a surface of #fe inches4 ,cut this strip diagonally1 giving two pieces in the shape of a triangle1 and measure exactly #e inches from the larger end of each strip and cut in two pieces4 ,take these strips and put them into the shape of an exact square1 and it will appear to be just #h inches each way1 or #fd inches--a loss of one square inch of superficial measurement with no diminution of surface4 ,illustration3 #e #ac #fe square inches4 #di4 ,if we buy #bj sheep for #bj shillings1 and give #bs4 for wethers1 #as4 #f;d4 for ewes1 and #d;d4 for lambs1 how many of each must we buy8 #ej4 ,a sets out from a place and travels #e miles an hour4 ,b sets out #d hours after ,a and travels in the same direction #c miles in the first hour1 #c miles the second hour1 #d miles the third hour1 and so on4 ,in how many hours will ,b overtake ,a8 ,,often ,,asked4 #ea4 ,what is the difference between #d square miles and #d miles square8 ,,to ,,tell ,,the ,,number ,,thought ,,of ,,on ,a ,,clock4 ,ask a person to think of any number on the dial of a clock2 you then point1 promiscuously at the various numbers1 telling the person to add the number of times you point to the number he thought of1 and when the total reaches #bj1 you will be pointing at the number he selected4 ,for instance1 suppose he selected the number #e4 ,you point indifferently #g times at the various numbers1 but the #hth time your pointer must be at ,,xii41 his addition will then be #ac 7for #e and #h added equal #ac71 the next at ,,xi41 his addition then #ad1 next at ,x41 and so on4 ,when he calls #bj1 you will be pointing at the number he thought of--#e4 ,illustration ,a very amusing experiment is to ask a person to write down the figures around the dial of a clock4 ,nearly all know that the figures are generally the ,roman numerals2 but1 in writing them down1 when they come to the four1 it is very often written ,,iv4 instead of ,,iiii4 ,it is said that a certain king1 being unable to find any other fault in a clock that had been constructed for him1 declared that the figure four should be represented by four strokes 7,,iiii7 instead of ,,iv4 ,in vain did the clock-maker point out the mistake1 for his majesty adhered obstinately to his own opinion1 and angrily ordered the alteration to be made4 ,this was done1 and the precedent thus formed has been followed by clockmakers ever since4 #eb4 ,at dinner table3 one great grandfather1 #b grandfathers1 #a grandmother1 #c fathers1 #b mothers1 #d children1 #c grandchildren1 #a great grandchild1 #c sisters1 #a brother1 #b husbands1 #b wives1 #a mother-in-law1 #a father-in-law1 #b brothers-in-law1 #c sisters-in-law1 #b uncles1 #c aunts1 #a nephew1 #b nieces1 and #b cousins4 ,how many persons8 8,can ,february ,march80 he asked4 8,no1 but ,april ,may10 was the reply4 8,look here1 old man1 you are out of ,june40 8,don't ,july about it40 8,it is not often one gets the better of your ,august personage40 8,ha6 now you have me ,noctober40 ,and then there was work for the coroner4 ,,pancake ,,day4 #ec4 ,on ,shrove ,tuesday last1 ,i'll tell you what pass'd ,in a neighbouring gentleman's kitchen1 ,where pancakes were making1 with eggs1 and with bacon ,as good as e'er cut off a flitchen4 ,the cook-maid she makes four lusty pancakes ,for ,william her favourite gardener1 8,pray be quick with that four10 cries ,jack1 8and make more1 ,for ,william won't let me go partner40 ,being sparing of lard1 the pan's bottom she marr'd ,in making the last of ,will's four2 ,so she said1 8,pr'ythee1 ,john1 run and borrow a pan1 ,or else ,i can't make any more40 ,jack soon got a pan1 but found by his span ,that the first was more wide than the latter1 ,this being a foot o'er1 whereas that before ,was three inches more and a quarter4 ,jack cries1 8,don't me cozen1 but make half a dozen4 ,for the pan is much less than before20 ,says ,will1 8,for a crown 7and ,i'll put the cash down7 ,your six will be more than my four40 8,tis done10 says brisk ,jack1 and his crown he did stake1 ,so both of them sent for a gauger2 ,the dimensions he takes1 of all their pancakes1 ,to determine this important wager4 ,he found1 by his stick1 they were equally thick1 ,so one of ,will's cakes he did take1 ,which he straight cut in twain1 twelve one-fifth#a the chord line2 ,and gave the less piece unto ,jack4 8,to the best of my skill10 says the gauger1 8this will ,make both of your shares equal and true20 ,will swore that he lied1 so1 the point to decide1 ,they refer themselves1 sirs1 unto you2 ,then pray give your answers1 as soon as you can1 sirs1 ,for what with their quarrels and jars1 ,we're afraid of some murder1 for no day goes over ,but they fight1 and are cover'd with scars6 ,illustration ,illustration ,illustration ,illustration #a ,inches4 ,a ,great ,prophet--#ajj per cent4 ,interesting ,items ,about the ,almanac4 ,the reason why ,february has only #bh days1 while the other months have #cj and #ca is attributable to the vanity of the ,emperor ,augustus4 ,his uncle and predecessor corrected the calendar1 arranging the year almost as we have it now2 he gave to the year #ab months1 or #cfe days4 ,the months were--,march 7the first month71 ,april1 ,may1 ,june1 ,quintilis1 ,sextiles1 ,september1 ,october1 ,november1 ,december1 ,january1 and ,february 7the latter being the last month of the year1 which among the ,romans had consisted originally of #aj months74 ,csar ordered that the year should begin with ,january1 and divided the days among them thus3 ,january1 ,march1 ,may1 ,quintilis1 ,september1 and ,november each had #ca days2 ,april1 ,june1 ,sextiles1 ,october and ,december had #cj days each2 and ,february 7the last month added to the year7 had #bi days regularly and a #cjth day every fourth year4 ,after ,julius ,csar's death1 ,mark ,antony changed the name of ,quintilis to ,july as we have it now4 ,augustus wanted a month for himself1 and wanted it as long as his uncle's month1 so he took ,sextiles for his and changed the name to ,august4 ,then he took ,february's #bith day and added it to ,august1 so that it might have #ca days2 and1 to avoid having #c months of #ca days each in succession1 ,september and ,november were reduced to #cj days1 and ,october and ,december increased to #ca days each4 ,previous to the year #ageb1 the legal year in ,england commenced on the #beth ,march4 ,in that year it was enacted that the legal year should begin on #ast ,january4 ,the change brought the calendar into unison with the actual state of the solar year4 ,it is curious that in ,scotland the change which made the legal year begin on ,january #ast was effected in #afjj4 ,for some time after the change in ,england1 legal documents contained two dates for the period intervening between #ast ,january and #beth ,march--that of the old year and that of the new4 ,during the time of ,oliver ,cromwell1 ,christmas ,day was described as a superstitious festival1 and put down in ,england by the strong hand of the law4 ,there has been a superstitious notion that ,fools' ,day dated back to the time of ,noah's ,ark4 ,the dove that was sent forth from the ,ark is supposed to have returned on ,april #ast4 ,,the ,,most ,,remarkable ,,month was ,february1 #ahff4 ,it had no full moon4 ,january had two full moons1 and so had ,march1 but ,february had none4 ,this had not occurred since the creation of the world1 and it will not occur again1 so scientists tell us4 ,all ,fools' ,day had it's origin in ,france1 before the time of the ,reformed ,calendar4 ,when the year commenced on ,march #beth1 the ,french frequently paid their ,new ,year's visits and bestowed their gifts on ,april #ast1 as ,march #beth occurred in ,passion ,week4 ,after the adoption of the new calendar1 however1 these ,new ,year's observances took place on ,january #ast1 and it was a common thing for people to forget the change of date4 ,pretended presents and mock ceremonial visits became common1 and the persons thus imposed on were known as ,april fish1 i4e41 a mackerel1 which1 like a fool1 is easily caught4 ,hence1 ,all ,fools' ,day4 #ed4 ,being at the summit of a tower #djj ft4 high1 ,i dropped a cricket ball from my hand1 causing it to alight on a ledge #bfj ft4 from the base1 over which it rolled and fell to the earth3 supposing that #a seconds were occupied by the rolling of the ball over the ledge1 how many seconds elapsed from the ball leaving my hand till it touched the earth1 and what was the acquired velocity at the moment of contact8 ,,practical ,,illustration4 ,in one of our great public schools a master known to successive generations of his pupils for fifty years as 8old ,buggus0 delighted in surprising his boys with strange sayings and doings4 ,on one occasion1 desirous of illustrating a question in the arithmetic lesson1 he said to a boy1 8,i am a tripe merchant1 and this platform is my shop4 ,you will come here and buy a pound of tripe4 ,now1 begin40 ,illustration 8,please1 ,i want a pound of tripe10 said a boy1 sauntering up4 8,where's your money80 demanded old ,buggus1 hoping to put the boy out of countenance4 8,where's your tripe80 was the ready retort2 but it gained for its unfortunate author four hours' detention on the next holiday4 #ee4 ,a syphon would empty a cistern in #dh minutes1 a tap would fill it in #cf4 ,how long will it take to fill the cistern when both taps are in action8 ,born to rule--a book-keeper4 8,,more ,,haste ,,less ,,speed40 #ef4 ,a compositor1 hurrying whilst setting up type for an arithmetic book--8,how to ,become ,quick at ,figures0--accidentally dropped the work of a problem2 unfortunately he mislaid the copy1 and all that he remembered was that both multiplicand and multiplier consisted of two figures4 ,the scattered type represented the following figures3--#a1 #b1 #c1 #c1 #d1 #f1 #g1 #h1 #h1 #i1 #i4 ,with the aid of a pencil and a piece of paper the compositor managed after a while to rearrange the figures in their proper place4 ,what was the problem8 ,illustration ,,profitable ,,carelessness4 ,a very amusing story is told of a harness-maker who lived some years ago in ,london4 ,he had a handsome saddle in his shop1 occupying a conspicuous position therein4 ,on his return from luncheon one day he observed that the saddle was gone4 ,calling to his foreman1 he said3 8,john1 who has bought the saddle80 8,i'm sure ,i don't know1 sir10 said the foreman1 scratching his head as if he were trying to think4 8,i cannot tell1 and the worst part of it is1 it hasn't been paid for4 ,while ,i was at work in the back of the shop a gentleman came in1 priced it1 decided to take it1 told me to charge it1 and throwing it into his trap1 drove off1 before ,i could think to ask his name40 8,that was very stupid of you10 said the harness-maker1 disposed to be angry at the man's carelessness4 8,very likely we have been robbed40 8,i don't think that sir10 said the foreman1 8for ,i'm very sure that the gentleman has traded here before40 8,well1 ,i can't afford to lose the money10 said the harness-maker4 8,we'll have to find out who took it and send him the bill4 ,ah60 he added1 with a smile1 after a moment's reflection1 8,i have it4 ,we'll charge it up to the account of every one of our customers who keep open accounts here4 ,those who didn't get it will refuse to pay1 so we shall be all right40 8,the book-keeper was instructed to do this1 and the bills in due course of time went out4 ,some weeks later the harness-maker asked the book-keeper if he had succeeded in discovering who the customer was4 8,no1 sir10 he replied1 8and we never shall1 ,i fear1 sir1 for about #dj people have paid for it already without saying a word40 ,a ,,cycle ,,catch4 ,tie a cord to the pedal of a bicycle1 such pedal to be the one that is the nearer to the ground1 and1 standing behind the back wheel1 pull the cord1 when1 strange as it appears1 the machine will come towards you1 although everyone would first imagine that the bicycle would move forward4 ,how is this8 ,illustration ,one ought to have dates at one's finger ends seeing they grow upon the palms4 ,,to ,,tell ,,the ,,spots ,,on ,,the ,,bottom ,,cards ,,of ,,six ,,heaps4 ,allow anyone to choose six cards from a full pack4 ,tell him the court cards count #aj1 and the other cards according to their pips4 ,having made his selection1 tell him to lay the chosen cards upon the table face downwards1 without allowing you to see them1 and to place upon each as many cards as pips are required to make #ab4 ,whilst he is doing so1 you should be out of the room or blindfolded4 ,on your return he hands you the cards left over1 and you have to tell the total number of spots on the six bottom cards4 ,suppose he had chosen #aj1 #f1 #a1 ,k1 #c and #g1 which totals #cg1 now on the #aj1 he would place two cards to make #ab2 on the #f1 he would place #f2 and on the #a1 #aa would be placed1 and so on4 ,on receiving the remaining cards from him you pretend to be looking through them carefully1 but you simply want to know how many he has given you1 which in the above example would be #aa4 ,to this number you add #bf1 which gives #cg1 the total spots required4 ,should there not be enough cards left on hand to complete the six heaps1 you can ask him how many cards he is short of1 and this number1 subtracted from #be1 will give the total4 ,it is better not to allow the person to choose six cards right off at the beginning1 but for him to shuffle and cut the pack as he pleases1 and to take the cards as they come4 ,,book-,,keeping ,,commandments4 ,by ,ledger laws1 what ,i receive ,is ,debtor made to those who give4 ,stock for my debts must ,debtor be1 and ,creditor by ,property4 ,profit and ,loss accounts are plain1 ,i ,debit loss and ,credit gain4 #eg4 ,how far does a man walk while planting a field of corn #bhe feet square1 the rows being #c ft apart from the fence8 ,a ,,matter ,,of ,,opinion4 ,a man walks round a pole on the top of which is a monkey4 ,as the man moves1 the monkey turns on the top of the pole1 so as still to keep face to face with the man4 ,now1 when the man has gone round the pole1 has he or has he not gone round the monkey8 ,illustration ,,try ,,it4 ,take the number #ae1 multiply it by itself1 and you have #bbe2 now multiply #bbe by itself1 then multiply that product by itself1 and so on until #ae products have been multiplied by themselves in turn4 ,the final product called for contains #ch1eci figures 7the first of which is #adab74 ,allowing three figures to an inch1 the answer would be over #ajgj feet long4 ,to perform the operation would require about #ej1jjj1jjj figures4 ,if they can be made at the rate of #ajj a minute1 a person working #aj hours a day for #cjj days in each year would be #bh years on the job4 ,,pathetic ,,advertising4 8,died1 on the #aath ultimo41 at his shop in ,fleet-street1 ,mr4 ,edward ,jones much regretted by all who knew and dealt with him4 ,as a man1 he was amiable2 as a hatter1 upright and moderate4 ,his virtues were beyond all price1 and his beaver hats were only #a #ds each4 ,he has left a widow to deplore his loss1 and a large stock to be sold cheap for the benefit of his family4 ,he was snatched to the other world in the prime of life1 and just as he had concluded an extensive purchase of felt1 which he got so cheap that the widow can supply hats at a more moderate charge than any house in ,london4 ,his disconsolate family will carry on his business with punctuality40 #eh4 ,in one corner of a hexagonal grass paddock each of the sides of which is #dj yards long1 a horse is tethered with a rope #ej yards long4 ,how many square yards can he graze over8 #ei4 ,a and ,b start together from the same point on a circular path1 and walk till they both arrive together at the starting point4 ,if ,a performs the circuit in #bbd seconds and ,b in #cfd seconds1 how many times do they each walk round8 8,,if40 ,if you could sell the sea at #a;d4 per #aj1jjj gallons1 it would bring in #aee billion pounds4 ,if you were to try and pump it dry1 at the rate of #a1jjj gallons per second1 it would take #ab1jjj million years4 ,there is always an 8if0 in these things6 #fj4 ,a lady met a gentleman in the street4 ,the gentleman said 8,i think ,i know you40 ,the lady said he ought1 as his mother was her mother's only daughter4 ,what relation was he8 ,illustration ,a ,,cricket 8,,catch40 #fa4 ,in an eleven1 when the ninth batsman goes in1 how many wickets have to fall before all are out8 #fb4 ,a boat's crew can row eight miles an hour in still water2 what is the speed of a river's current if it takes them #b hours and #dj minutes to row #h miles up and #h miles down8 ,,bad ,,writing4 ,in a well-known firm in ,sydney the clerks are presided over by a rather impetuous manager1 whose violent fits of temper very often dominate his reason4 ,for instance1 the other day he was wiring into one of them about his bad work4 8,look here1 ,jones10 he thundered1 8this won't do4 ,these figures are a perfect disgrace to a clerk6 ,i could get an office boy to make better figures than those1 and ,i tell you ,i won't have it6 ,now1 look at that five1 it looks just like a three4 ,what do you mean1 sir1 by making such beastly figures8 ,explain60 8,i--er beg your pardon1 sir10 suggested the trembling clerk1 his heart fluttering terribly1 8but--er well1 you see1 sir1 it is three40 8,a three80 roared the manager2 8why1 it looks just like a five60 #fc4 ,write #bd with three equal figures1 neither of them being #h4 ,,the ,,wrong ,,column4 #fd4 ,a clerk1 while posting from day book to ledger1 transposed an amount by placing the pence in the shilling column and the shillings in the pence column1 thereby causing an error of #is4 #b;d4 ,with what amount could he make such a mistake8 ,,educational ,,vagaries4 ,extracts from ,reports of ,country ,provisional ,schools4 ,school ,no4 #a3 ,on roll1 #a boy1 #a girl2 total1 #b4 ,average attendance1 #jf boy1 #jf girl2 total1 #ab4 ,school ,no4 #b3 ,on roll1 #b boys1 #b girls2 total #d4 ,average attendance1 #af boys1 #ac girls2 total1 #bi4 ,school ,no4 #c3 ,on roll1 #b boys1 no girls4 ,average attendance1 #jh boys4 ,by the above we see the public are paying for a teacher to provide education for eight-tenths of a boy6 #fe4 ,three-fourths of a cross1 and a circle complete1 ,two semi-circles at a perpendicular meet2 ,next add a triangle which stands on two feet1 ,two semi-circles and a circle complete4 ,a ,,dispute4 #ff4 ,two men have an equal interest in a grindstone1 which is #e ft4 #f in4 in diameter4 ,the centre of the stone1 to the extent of a diameter of #ah in41 is useless1 and not to be taken into account4 ,required to find the depth to which the first partner may be allowed to grind away from the stone in order to leave an equal share of the stone to the second partner4 ,illustration ,,bank ,,note ,,verse4 ,on the backs of bank notes one sometimes meets with strange and peculiar sentiments4 8,go1 poor devil1 get thee gone10 is the kind of parting salutation most in favour2 but the following is chiefly notable as a rare instance of the bank-note rhymester parting with his money in a ,christian spirit3 ,farewell1 my note1 and wheresoe'er ye wend1 ,shun gaudy scenes1 and be the poor man's friend2 ,you've left a poor one--go to one as poor2 ,and drive despair and hunger from his door4 ,an ,irish merchant1 who felt annoyed at a complaining letter he received from a customer1 wrote back3--8,we decline to acknowledge the receipt of yours of the #aeth40 ,if to-day is the to-morrow of yesterday1 is to-day the yesterday of to-morrow8 #fg4 ,suppose that four poor men build their houses around a pond1 and that afterwards four evil-disposed rich men build houses at the back of the poor people--as shown in illustration--and wish to have a monopoly of the water3 how can they erect a fence so as to shut the poor people off from the pond8 ,illustration ,,some ,,trade ,,signs ,,and ,,mottoes4 ,many curious inscriptions are to be found displayed on shop windows1 office doors1 etc4 ,here are a few3-- ,a ,pawnbroker4--8,mine is a business of the greatest interest40 ,a ,flourishing ,bootmaker4--8,don't you wish you were in my shoes80 ,a ,publican4--8,good beer sold here1 but don't take my word for it40 ,a ,hairdresser4--8,two heads are better than one40 ,a ,carter4--8,excelsior--hire and hire40 ,a ,baker4--8,the staff of life ,i do supply1 by it you live and so must ,i40 ,a ,butcher4--8,we kill to dress1 not dress to kill40 ,a ,builder4--8,i send innocent men to the #8scaffold4'0 ,a ,clerk4--8,i possess more pens than pounds40 ,a ,dentist4--8,i look #8down in the mouth' and am happy40 ,a ,doctor4--8,i take pains to remove pains40 ,a ,hatter4--8,i shelter #8the heir apparent' and protect #8the crown4'8 ,a ,photographer4--8,mine is a developing business and mounting rapidly40 ,a ,solicitor4--8,i study the law--and the profits40 ,an ,undertaker4--8,no complaints from our customers40 ,,rival ,,butchers4 ,t4 ,,jones4--8,sausages1 #c;d4 per lb4--to pay more is to be robbed40 ,j4 ,,smith4--8,sausages1 #d;d4 per lb4--to pay less is to be poisoned40 ,a ,french confectioner1 proud of his ,english1 and wishing to let his customers know that their wants would be attended to without delay1 put out the notice1 8,short weights here40 ,a shopkeeper in the old country had printed under his name 8,the little rascal40 ,when asked the meaning of this strange sign1 he replied1 8,it distinguishes me from the rest of my trade1 who are all great rascals40 ,on an ,office ,door4--8,shut this door1 and as soon as you have done talking on business1 serve your mouth the same way40 8,,she40 #fh4 ,a country spark addressed a charming 8she10 ,in whom all lovely features did agree2 ,but being void of numbers1 as doth show1 ,desirous was the lady's age to know4 8,my age is such that if multiplied by three1 ,two-sevenths of the product triple be3 ,the square root of two-ninths of that is four2-- ,tell me my age or never see me more40 ,illustration ,,running ,,short4 #fi4 ,a vessel on a #c months' trip has provisions for #d months1 but the stores are served out as if the voyage had to be completed in #c months4 ,at the end of #b months1 it is discovered that the voyage will take #c months4 ,to what proportion must the rations be reduced for the remaining time8 ,in a certain town in the ,north of ,queensland1 a class of young men was formed to receive lessons in short methods of business arithmetic4 ,the teacher was endeavouring to knock into the head of a young man that the cost of a dozen articles is the same number of shillings that a single article costs in pence4 ,to illustrate the rule1 he gave the following example3-- 8,if ,i buy #a dozen apples at #a;d each1 then the dozen will cost #a shilling2 and if ,i buy #a dozen oranges at #b pence each1 the dozen will cost #b shillings4 ,now1 supposing ,i buy #a dozen at #c pence each1 how much will the dozen cost80 ,,young ,,man 7after two minutes' reflection7--8,are they apples or oranges80 ,a ,,draughts ,,puzzle4 #gj4 ,ten draughtsmen are placed in a row4 ,the puzzle is to lift one up and passing over two at a time 7neither more nor less7 to place it on the top1 or to 8crown0 the next one1 continuing in this fashion until all are crowned4 ,in passing over a piece already crowned1 it is to be reckoned as two pieces4 #ga4 ,in the centre of a pond #bj feet square there is a small island1 on which is growing a tree4 ,two boys notice there is a bird's nest on the top of the tree1 but the difficulty is to reach the island1 as they have #b short planks that only measure #h feet each4 ,after a little while they hit on an ingenious plan1 and1 without nailing the planks together1 manage to place them so they can reach the tree in safety4 ,how did they do it8 ,,teacher--8,now1 ,i want all the children to look at ,tommy's hands1 and see how clean they are1 and see if all of you cannot come to school with cleaner hands4 ,tommy1 perhaps1 will tell us how he keeps them so nice80 ,,tommy--8,yes 'm2 mother makes me wash the breakfast things every morning40 ,,brain-,,bewilderers4 ,an amusing periodical got up by the boys of a certain college gives a capital skit on the style of examination-papers frequently presented for the torture of pupils4 ,here are a few examples3-- ,supposing the ,river ,murray to be three cubits in breadth--which it isn't--what is the average height of the ,alps1 stocks being at nineteen and a-half8 ,if in autumn apples cost fourpence per pound in ,melbourne1 and potatoes a shilling a score in spring1 when will greengages be sold in ,brisbane at three-halfpence each1 ,sydney oranges being at a discount of five per cent48 ,if two men can kill twelve kangaroos in going up the right side of a rectangular turnip-field1 how many would be killed by five men and a terrier pup in going down the other side8 ,if a milkmaid four feet ten inches in height1 while sitting on a three-legged stool1 took four pints of milk out of every fifteen cows1 what was the size of the field in which the animals grazed1 and what was the girl's name1 age1 and the occupation of her grandfather8 ,if thirty thousand millions of human beings have lived since the beginning of the world1 how many may we safely say will die before the end of it8 ,n4,b4--,this example to be worked out by simple subtraction1 algebra1 and the rule of three4 ,compare results4 #gb4 ,find two numbers in the proportion of #i to #g such as the square of their sum shall be equal to the cube of their difference4 ,,arithmetical ,,thought ,,reading4 ,a great deal of fun can be derived from puzzles of this nature--they are endless in variety--and as they depend upon some principle in arithmetic should be easily remembered4 ,example #a4 ,think of a number1 say #e ,double it #aj ,add #e #ae ,add #ab #bg ,take away #c #bd ,halve it #ab ,take away number first thought of--#e ,the answer will always be #g ,example #b4 ,think of a number1 say #h ,square it #fd ,subtract the square of the number which is #a less than the number thought of--that is #g--whose square is #di--leaves #ae ,add #a #af ,when this last number is told1 halve it1 and you will arrive at the original number--#h4 ,example #c4 ,think of a number1 say #i ,multiply by #c #bg ,add #b #bi ,multiply by #c #hg ,add #b more than the number thought of 7#aa7 #ih ,the number of tens in the last answer gives the number thought of1 viz41 #i4 ,example #d4 ,think of a number1 say #g ,multiply by #c #ba ,if product be odd add #a #bb ,halve it #aa ,multiply by #c #cc ,if product be odd add #a #cd ,halve it #ag ,ask how many #i's are in the remainder1 when1 of course1 the reply will be #a4 ,the secret is to bear in mind whether the first sum be odd or even4 ,if odd first time1 retain #a in the memory2 if odd a second time1 #b more1 making #c2 to which add #d for every #i contained in the remainder4 ,in the above example1 there being only one #i in #ag1 this gives us #d1 which added to #c produces the number thought of--#g4 ,when even simply add #d for every #i in remainder4 ,,how ,,to ,,tell ,,the ,,age ,,of ,a ,,person4 ,tell a person to write down the figure which represents the day of the week on which he was born2--thus1 #a for ,sunday1 #b for ,monday1 and so on2 next1 the figure for the month--#a for ,january1 #b for ,february1 c42 then the date of the month2 now tell him to multiply the number thus formed by #b1 add #e1 multiply by #ej1 and then to add his age1 and from this sum to subtract #cfe2 now you ask him for the remainder1 to which you secretly add #aae4 ,the result will be3--,the first figure1 the day of the week2 the next1 the month in the year2 the next1 the date of the month2 and the last1 the age in years4 ,example3 ,a person was born on ,wednesday1 #aath ,june1 #ahfc4 ,write #d1 as ,wednesday is #dth day of the week4 #f1 as ,june is #fth month of year4 #aa1 as that is the date given1 #aath ,june4 ,the figures then are-- #dfaa #b ---- #ibbb #e ---- #ibbg #ej ------ #dfacej #ce ,age ------ #dfache #cfe ------ #dfajbj #aae -------- #d-f-aa-ce ,a ,,good ,,figure ,,trick4 ,tell a person to set down a sum of money less than #ab1 in which the pounds exceed the pence2 next to reverse this amount1 making pence pounds1 etc41 and to subtract the one from the other1 then set beneath the result itself reversed1 adding the last two lines together1 when you will tell him the result1 which will always be #ab #ahs4 #aa;d4 ,example3 #aj #h #g #g #h #aj -------- #b #ai #i #i #ai #b -------- #ab #ah #aa ,if the performer be blindfolded the trick looks very mystifying2 he should not1 however1 repeat it1 for many would soon discover the secret1 but as the peculiarity is not confined to money1 other illustrations can be given if required--for instance--if a number of yds41 ft4 and inches 7less than #ab yds47 be operated on1 the final answer will always be #ab yds4 #a ft4 #aa inches2 and if a number of cwts41 qrs4 and lbs4 7less than #bh cwts47 be chosen1 the answer will always be #bh cwts4 #b qrs4 #bg lbs4 8,girls0 and 8,boys40 ,at a school examination1 the inspector set the girls to write an essay on 8,boys0 and the boys to write one on 8,girls40 ,the following was handed in by a girl of #ab3-- 8,the boy is not an animal1 yet they can be heard to a considerable distance4 ,when a boy hollers he opens his big mouth like frogs1 but girls hold their tongues till they are spoken to1 and then they answer respectable1 and tell just how it was4 ,a boy thinks himself clever because he can wade where it is deep1 but ,god made the dry land for every living thing1 and rested on the seventh day4 ,when the boy grows up he is called a husband1 and then he stops wading and stays out at nights1 but the grew up girl is a widow and keeps house40 ,one of the boys sent in3-- 8,girls are very stuck up and dignified in their manners and behaveyour4 ,they make fun of boys1 and then turn round and love them4 ,girls are the only people that have their own way every time4 ,girls is of several thousand kinds1 and sometimes one girl can be like several #ajjj girls if she wants anything4 ,i don't beleive they ever killed a cat or anything4 ,they look out every nite and say1 8,oh1 ain't the moon lovely60 ,thir is one thing ,i have not told1 and that is they always now their lessons bettern boys4 ,this is all ,i now about girls1 and father says the less ,i now the better for me40 #gc4 ,the sum of the squares of two consecutive numbers is #aaje4 ,what are the numbers8 ,a ,,problem ,,for ,,plumbers4 #gd4 ,a requires a tank in size capable of holding the quantity of water that would be caught from the roof of his house in a fall of #c inches of rain4 ,the roof 7commonly called a 8hip-roof07 is at an angle of #de degrees to the wall plates4 ,the length of house is #cj ft41 breadth #bd ft41 and length of ridge to roof #f ft4 ,but the eaves of the iron used for the roofing were so large as to increase its 7the roof's7 dimensions by #c inches all round1 and the spouting added another #c inches all round4 ,find the number of gallons the tank would require to contain2 also dimensions of tank to be made so that its height must exceed its diameter by no more than #ab inches8 8,the 'embers of a dying year0--,november1 ,december4 ,,to ,,tell ,,the ,,compass ,,by ,a ,,watch4 ,hold the watch face-downwards above your head with the hour hand pointing towards the sun1 and half-way between the hour hand and the figure ,,xii will be the ,north4 #ge4 ,divide #ajj into two parts1 so that a quarter of one exceeds one-third of the other by #aa4 ,,strange ,,but ,,true4 #gf4 ,two persons were born at the same place at the same moment of time2 after an age of #ej years they both died also at the same place and at the same instant1 yet one had lived #ajj days more than the other4 ,how was this remarkable event achieved8 ,,astronomical4 #gg4 ,the planet ,jupiter is five times further from the sun than our earth1 and #acca times larger4 ,assuming that the diameter of the earth is #giab miles1 find ,jupiter's diameter1 circumference and area4 ,,an ,,unsolved ,,problem4 ,one of the commercial questions of the day which remains to this time unsettled1 is whether the fact of a gentleman having ,,no ,,tin may not have something to do with the answer he invariably sends of ,,not ,,in when anyone calls on him with a bill4 #gh4 ,find nine numbers in arithmetical progression--common difference #c--whose sum is equal to #efgj1 and arrange in a square1 each side containing three different numbers1 so that1 when added vertically1 horizontally or diagonally1 the sum of each three numbers will amount to #ahij4 #gi4 ,i have a box4 ,the pieces forming the sides are #e ft long1 and those forming the ends are #d ft4 broad4 ,the box1 when measured externally all round1 measures #ah ft #d in41 and when measured all round internally1 measures #ag ft #h in4 ,how can this be8 ,illustration ,teacher3 8,who was it that supported the world on his shoulders80 ,bright ,pupil3 8,it was ,atlas1 ma'am40 ,teacher3 8,and who supported ,atlas80 ,bright ,pupil3 8,the book don't say1 but ,i s'pose it was his wife40 ,,on ,,both ,,sides ,,of ,a ,,door ,,in ,a ,,melbourne ,,office4 ,,the ,,man ,,who ,,forgets ,,the ,,door4 ,oh1 there's an individual who ev'rywhere abounds1 ,thro' trains and shops and offices he makes his busy rounds1 ,and in and out for ever he is going o'er and o'er1 ,to keep somebody after him attending to the door6 ,in sultry summer1 when to catch a cooling breeze we've tried1 ,and carefully have opened every door and window wide1 ',tis then you may be certain as he vanishes from sight1 ,he'll die but that he'll shut the door--and close it very tight6 ,but when the winds of winter come1 with cold and biting breath1 ,oh1 then it is the awful wretch is tickled 'most to death6 ,his sense of pleasure reaches to a point that is sublime2 ,he never fails to leave the door wide open every time6 #hj4 ,a man agrees to work for #h a year and a suit of clothes4 ,he left at the end of seven months1 and received #b #acs4 #d;d4 and his clothes4 ,what is the value of the suit8 #ha4 ,a bought four horses for #abj4 ,for the second he gave #c more than for the first1 for the third #b more than for the second1 and for the fourth #f more than the third4 ,find price of each4 #hb4 ,with eight pieces of card of the shape of figure ,a1 four of figure ,b and four of figure ,c1 and of proportionate sizes1 form a perfect square4 ,illustration #hc4 ,place four #e's so that they shall express #f4 8,,she0 ,,again4 #hd4 ,the country spark that asked the charming 8she0 ,how many years of age that she might be1 ,again asked her to tell to him in haste ,how many inches she was round the waist4 8,my waist is such if multiplied by four1 ,four-fifths of product add on my age more1 ,the square root of three-fifths of this is six3 ,now find my waist1 and get out of this fix40 ,,some ,,long ,,words4 ,the eight longest words in the language are philoprogenitiveness1 incomprehensibleness1 disproportionableness1 transubstantiationalist1 suticonstitutionalist1 honourifibilitudinity1 velocipedestrianistical1 and proautionsubstantionist4 ,the last four are not found in the best dictionaries1 but that most hideous word1 8,dacryocystosyringokatakleisis10 is in some of the new lexicons4 ,,his ,,own ,,grandfather4 ,the complication of relationship brought about by marriage is the cause of many a family squabble1 but it is seldom one hears of fatal results attending such matters4 ,according to an ,american newspaper1 a resident of ,pennsylvania committed suicide a few days ago from a melancholy conviction that he was his own grandfather4 ,the following is a copy of a singular letter he left3--8,i married a widow who had a grown-up daughter4 ,my father visited our house very often1 fell in love with my step-daughter1 and married her4 ,so my father became my son-in-law and my step-daughter my mother1 because she was my father's wife4 ,some time afterwards my wife had a son2 he was my father's brother-in-law and my uncle1 for he was the brother of my step-mother4 ,my father's wife--i4e41 my step-daughter--had also a son2 he was1 of course1 my brother1 and in the meantime my grandchild1 for he was the son of my daughter4 ,my wife was my grandmother1 because she was my mother's mother4 ,i was my wife's husband and grandchild at the same time4 ,and as the husband of a person's grandmother is his grandfather1 ,i was my own grandfather40 ,thus he died1 a martyr to his own existence4 ,illustration #he4 ,if #ajj stones are placed on the ground1 in a straight line1 at the distance of #a yard from each other1 how far will a person travel who will bring them all1 one by one1 to a basket placed one yard from the first stone8 ,a little boy1 writing a composition on the zebra1 was requested to describe the animal and to mention what it was useful for4 ,after deep reflection1 he wrote3--8,the zebra is like a horse1 only striped4 ,it is chiefly useful to illustrate the letter ,z40 #hf4 ,i bought a horse and sold him again at #e per cent4 on my purchase2 now1 if ,i had given #e per cent4 less for the horse1 and sold him for #as4 less1 ,i would have gained #aj per cent4 ,what was the original cost8 #hg4 ,find three numbers such that the first with half of the other two1 the second with one-third of the other two1 and the third with one-fourth of the other two1 shall be equal to #cd8 ,,the ,,famous 8#de0 ,,puzzle4 #hh4 ,take #de from #de1 and leave #de as a remainder4 ,there are at least two ways of doing this4 #hi4 ,how can #de be divided into #d such parts that if you add #b to the first part1 subtract #b from the second part1 multiply the third part by #b1 and divide the fourth part by #b1 the sum of the addition1 the remainder of the subtraction1 the product of the multiplication1 and the quotient of the division are equal8 #ij4 ,the square of #de is #bjbe1 if we halve this we get #bj_/be and #bj plus #be equals #de4 ,find two other numbers of four figures that produce the same peculiarity4 #ia4 ,a mother of a family being asked how many children she had1 replied3 8,the joint ages of my husband and myself are at present six times the united ages of our children2 two years ago their united ages were ten times less than ours1 and in six years hence our joint ages will be three times theirs40 ,how many children had she8 ,,where ,,the ,,creeds ,,agree4 ,the ,mahometans1 ,christians and ,jews1 with different creeds1 are all striving to reach the same place--,heaven4 ,now1 we will endeavour to show1 by figures1 that it is possible for them all to accomplish their purpose4 ,the figures #d1 #e1 #f1 at the angles of the large triangle1 represent respectively the above mentioned sects4 ,they are very distant from each other1 but we will induce them to meet half-way4 ,thus1 the ,mahometans and ,jews meet at #aj1 the ,mahometans and ,christians at #i1 and the ,jews and ,christians at #aa2 and by joining these totals to the opposite numbers we see they all meet at last in ,heaven 7#ae74 ,it should be mentioned that any numbers whatever may be used to represent the sects1 but the result will always be the same4 ,illustration 8,,she0 ,,once ,,more4 #ib4 ,the country spark again addressed the charming 8she40 ,this time he wished to know her height4 ,she replied1 8,my height 7in inches7 if divided by the product of its digits1 gives as quotient #b1 and the digits are inverted by adding #bg40 8,you have a bright look1 my boy10 said the visitor at the school4 8,yes1 sir10 replied the candid youth2 8that's because ,i forgot to rinse the soap off my face this morning40 ,,his ,,last ,,will ,,and ,,testament4 #ic4 ,a father on his death-bed gave orders in his will that if his wife1 who was then pregnant1 brought forth a son1 he should inherit two-thirds of his property1 and the mother the remainder2 but if she brought forth a daughter the latter should have only one-third1 and the mother two-thirds4 ,the widow1 however1 was delivered of twins1--a boy and a girl4 ,what share ought each to have of the property left by the father1 who had his life insured in the ,australian ,mutual ,provident ,society for #g1jjj4 ,illustration #id4 ,money lent at #f per cent ,to those who choose to borrow2 ,how long before ,i'm worth a pound ,if ,i lend a crown to-morrow8 ,a ,,keen ,,eye ,,to ,,business4 ,upon the death of the senior partner of an ,australian firm a notice of the sad event was sent to1 amongst others1 a ,german lithographic establishment4 ,the clerk in this ,german house1 who was instructed to answer the communication1 wrote the following letter of condolence3-- 8,we are greatly pained to hear of the loss sustained by your firm1 and extend to you our heartiest sympathy4 ,we notice the circular you sent us announcing ,mr4 ,s----'s death is lithographed by ,messrs4----4 ,we regret that you did not see your way to let us estimate for the printing of the same4 ,the next time there is a bereavement in your house we will be glad to quote you for the lithographic circulars1 and are confident that we can give you better work at less cost than anybody else in the business4 ,trusting that we may soon have an opportunity of quoting you our prices1 we remain1 with profound sympathy1 yours truly1----40 ,an ,american journal1 describing a new counterfeit bank-note1 says the vignette is 8cattle and hogs1 with a church far in the distance0--a good illustration of the world4 #ie4 ,on a square piece of paper mark #ab circles as shown in diagram4 ,the puzzle is to divide the figure into four pieces of equal size1 each piece to be of the same shape1 and to contain three circles1 without getting into any of them4 ,illustration ,,the ,,origin ,,of ,,the 8,,stone40 ,measurement of weight by the 8stone0 arose from the old custom farmers had of weighing wool with a stone4 ,every farmer kept a large stone at his farm for this purpose4 ,when a dealer came along he balanced a plank on top of a wall1 and put the stone on one end of it and the bags of wool on the other1 until the weights were equal4 ,at first the stones were of all sorts and sizes and weights1 with the result that dealers who wished to make a living had to be remarkably knowing in their estimates of them4 ,the many inconveniences involved by this inequality resulted in all stones being made of a uniform weight as far as wool was concerned4 ,the weight of a stone of potatoes1 meat1 glass1 cheese1 c41 all differ4 ,a little boy was reading in his ,scottish history an account of the battle of ,bannockburn4 ,he read as follows3 8,and when the ,english army saw the new army on the hill behind1 their spirits became damped40 ,the teacher asked him what was meant by 8damping their spirits10 and the boy1 not comprehending the meaning1 simply answered1 8,putting water in their whisky40 ,,thunder ,,and ,,lightning ,,calculation4 #if4 ,between the earth and a thundercloud there are four currents of air1 having a temperature of #hg1 #eg1 #dg1 and #cg degrees respectively4 ,the first current is half the depth of the second1 the second half the third1 and the third half the fourth4 ,if a peal of thunder is heard #b-cbea_/dbef seconds after the lightning flash1 find the depth of the fourth current and the time occupied by the sound in passing through it4 #ig4 ,first cut out1 with a pen-knife1 in paste-board or card1 ,the designs numbered #a1 #b and #c1 ,four of each2 after which1 as the puzzle is hard1 ,you had better be guided by me ,to a certain extent2 for1 in fixing1 take care ,that each portion is fitted in tight1 ,or they will not produce such a neat little square ,as they otherwise would if done right4 ,illustration ,,quite ,,proper4 8,what is a propaganda10 inquired the teacher4 ,the boy looked at the ceiling1 wrinkled his forehead1 wrestled with the question a minute or two1 and then answered that it was the brother of a proper goose4 ,,december ,,and ,,may4 #ih4 ,an old man married a young woman2 their united ages amounted to #ajj2 the man's age1 multiplied by #d and divided by #i gives the woman's age4 ,what were their respective ages8 #ii4 ,a and ,b set out on a walking expedition at the same time--,a from ,melbourne to ,geelong1 and ,b from ,geelong to ,melbourne4 ,on reaching ,geelong ,a immediately starts again for ,melbourne4 ,now1 ,a arrives at ,geelong four hours after meeting ,b1 but he reaches ,melbourne three hours after their second meeting4 ,in what time did each perform the journey8 #ajj4 ,what two numbers are those of which the square of the first plus the second equals #aa1 and the square of the second plus the first equals #g8 ,a schoolmaster1 describing a money-lender1 says1 8,he serves you in the present tense1 he lends you in the conditional mood1 keeps you in the subjunctive mood1 and ruins you in the future40 #aja4 8,how much money have ,i10 says a father to his son4 ,son replied1 8,they don't teach prophecy at our school40 8,well1 they teach arithmetic1 ,i suppose10 rejoined the father1 smartly2 8if you multiply one-half1 one-third1 one-fourth1 one-sixth1 three-quarters1 and two-thirds of my money together1 the product will be #ajcfh4 ,now find out how many pence ,i have40 #ajb4 ,a person has #abfj quarters of wheat4 ,he sells one-fifth at a gain of #e per cent41 one-third at a gain of #h per cent41 and the remainder at a gain of #ab per cent4 ,had he sold the whole at a gain of #aj per cent4 he would have made #bc #bs4 more than he did4 ,find the cost price of one quarter4 #ajc4 ,is the word 8with0 ever used as a noun8 ,,the ,,great ,,puzzle ,,of ,,the ,,century4 #ajd4 ,place the nine digits 7#a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i7 together in such a manner that they will make #ajj4 #aje4 ,also make #ajj by using the cipher in addition to the digits4 #ajf4 ,how far apart should the knots of a log-line be to indicate every half-minute1 a speed of one mile per hour8 #ajg4 ,several persons are bound to pay the expenses of a law process1 which amount to #hjj1 but three of them being insolvent1 the rest have #fj each to pay additional4 ,how many persons were concerned8 #ajh4 ,if five times four are thirty-three1 ,what will the fourth of twenty be8 #aji4 ,a locomotive with a truck is travelling over a straight level line at the rate of #fj miles an hour4 ,a man standing at the extreme rear of the truck casts a small stone into the air in a perpendicular direction4 ,the stone travels upward at an average rate of #cj feet per second for #c seconds2 the height of the man's hand from ground when the stone leaves is #ae feet4 ,at what distance behind the train will the stone strike the ground in its descent8 ,a ,tombstone in an ,english ,cemetery4 ,many quaint and puzzling epitaphs are often to be seen engraved on several of the tombstones in some of the old cemeteries at ,home4 ,the adjoining illustration represents a tombstone in the old burial-ground of ,london--,kensal ,green4 ,it might 8liven0 up the reader to discover the scheme of kindred as given in the inscription4 ,illustration3 ,,sacred ,,to ,,the ,,memory ,,of ,,two ,,grandmothers ,,with ,,their ,,two ,,granddaughters2 ,,two ,,husbands ,,with ,,their ,,two ,,wives2 ,,two ,,fathers ,,with ,,their ,,two ,,daughters2 ,,two ,,mothers ,,with ,,their ,,two ,,sons2 ,,two ,,maidens ,,with ,,their ,,two ,,mothers2 ,,two ,,sisters ,,with ,,their ,,two ,,brothers ,,yet1 ,,but ,,six ,,corpses ,,in ,,all ,,lie ,,buried ,,here-- ,,all ,,born ,,legitimate ,,from ,,error ,,clear4 ,,easily ,,answered4 8,johnny10 said his teacher1 8if your father can do a piece of work in seven days1 and your uncle ,george can do it in nine days1 how long would it take both of them to do it80 8,they'd never get it done10 said ,johnny2 8they'd sit down and tell snake-yarns40 #aaj4 ,a well is to be sunk by #ab men1 in groups of #d each1 in #ab days4 ,the groups work in the ratio of #f1 #g1 and #h2 when half the task is done rain sets in and prevents them working for #b days1 in which time one man of the first1 #b of the second1 and #c of the third group go away1 leaving the remainder to finish the job4 ,what extra time did they work8 8,,take ,,care ,,of ,,the ,,pence1 c40 ,one of the most startling calculations is the following3-- ,a penny at #e per cent4 compound interest from ,a4,d4 #a to #ahij would amount to #aj1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj1jjj1 jjj1jjj1jjj1 i4e41 ,ten ,sextillions of pounds1 or more money than could be contained in ,one ,thousand ,millions of ,globes each equal to the ,earth in magnitude1 and all of solid gold4 #aaa4 ,on a flagstaff consisting of an upright pole 7#f feet of which is underground7 is a cross-yard #bd feet long2 the latter is fixed at a distance of one-third of the length of the visible part of the pole from the top2 passing from the top of the pole to the ends of the yard are ropes1 forming stays whose falls or ends reach to the ground on either side of the pole1 and it is found that these falls just reach the base of the pole4 ,the total length of rope in the aforesaid stays is #dj feet4 ,supposing that the top diameter of the pole is one-third of that at the extreme base1 and that the whole length of rope used is #ed1agg times the base diameter of the pole1 what would the pole cost at #a penny per #ajj cubic inches8 ,,teacher--8,your writing is fairly good1 but how do you account for making so many mistakes in your spelling80 ,,scholar--8,please1 ma'am1 ,i had chilblains on my hand80 #aab4 ,put down #d marks 7 71 and then require a person to put #e more marks and make #aj4 8,,keep ,,your ,,hair ,,on40 #aac4 ,supposing there are more persons in the world than anyone has hairs on his head1 there must be at least two persons who have the same number of hairs on the head to a hair4 ,explain this4 #aad4 ,show what is wrong in the following3-- #h-h #b-b1 dividing both these equals by #b-b the result must be equal2 #h-h divided by #b-b #d1 and #b-b divided by #b-b #a1 therefore1 since the quotients of equals divided by equals must be equal1 #d must be equal to #a4 8,,glad ,,tidings40 ,many will be surprised to hear that there is ,scriptural authority for advertising4 ,advertising not only has ,scriptural authority1 but it is of very respectable antiquity as well4 ,if you will look in ,numbers ,,xxiv41 #ad1 you will find ,balaam saying 8,come now1 and ,i will advertise10 and ,boaz says in ,ruth ,,iv41 #d1 8,and ,i thought to advertise40 ,,optical ,,illusions4 ,illusions of the ,eye are numberless1 and afford a wide field for experiment4 ,some people are left-eyed1 others right-eyed1 and very few use both eyes equally4 ,it is impossible to tell how far they really do deceive us unless they have been tested in the proper manner4 ,for instance1 if you ask anyone to what height a bell-topper would reach if placed on the floor against the wall1 nine times out of ten the height guessed will be half as much again as the real height of the hat4 ,everyone seems to over-estimate the proper height4 ,illustration ,another favourite illusion is to ask a person to mark on the wall a height from the floor which would represent the length of a horse's head3 here the majority guess far too little--for a horse's head is much longer than most people imagine1 ranging from #be to #cd inches4 ,in a recent experiment #e persons out of #f under-estimated the proper height4 ,illustration ,here are two triangles4 ,which is the one whose centre is the better indicated8 7,it looks like ,a1 but it is ,b74 ,illustration ,again3 ,out of the two straight lines ,c and ,d which is the longer8 7,by measurement we see they are both the same74 ,illustration ,guess1 by eye-measurement only1 the longest and shortest of the three lines marked ,a ,a1 ,b ,b1 and ,c ,c4 ,when you have done guessing measure1 and see how much you are out4 ,illustration ,which is the tallest gentleman of the three appearing in adjoining figure8--,many would imagine the last to be the tallest1 and the first the shortest1 whereas the reverse is the case--the last is the shortest1 and the first the tallest4 ,illustration ,it is surprising how the eye can be deceived1 when dealing with areas or circles4 ,place on the table a half-crown and a threepenny-piece2 let these be1 say1 #i or #aj inches apart1 and ask a friend how many of the latter can be placed on the former--with this proviso3 the threepenny-pieces must not rest on each other1 nor must they overlap the outer rim of the half-crown2 they must be fairly within the circumference of the larger coin4 ,many will answer #f1 #e1 or #d1 others who are more cautious #c4 ,try for yourself and see how many you can put on1 and you are sure to be surprised4 ,,are ,,these ,,lines ,,parallel8 ,the 8herring-bone0 figure here illustrated is yet another proof that our eyes are faulty4 ,the horizontal lines appear to slant in the direction in which the short intersecting lines are falling1 and would give one the idea that they would meet if continued1 whereas really they are parallel4 ,the illusion is more striking if you tilt the leaf up4 ,illustration ,,how ,,did ,,he ,,do ,,it4 #aae4 ,once there was an old tramp who had to go through a tollbar1 and before he could get through he had to pay a penny4 ,he had not a penny2 he did not find a penny1 nor borrow a penny1 nor steal nor beg a penny1 and yet he paid a penny and went through4 #aaf4 ,find a number which is such that if four times its square be diminished by #f times the number itself the remainder shall be #gj4 #aag4 ,a man has a certain number of apples2 he sells half the number and one more to one person1 half the remainder and one more to a second person1 half the remainder and one more to a third person1 half the remainder and one more to a fourth person1 by which time he had disposed of all that he had4 ,how many had he8 ,,teacher 7impressing one of her protgs7--8,be brave and earnest and you will succeed4 ,do you remember my telling you of the great difficulty #8,george ,washington' had to contend with80 ,,willy ,,raggs--8,yes1 mum2 he couldn't tell a lie40 #aah4 ,two numbers are in the ratio of #b and #c1 and if #i be added to each they are in the ratio of #c to #d4 ,find the numbers4 ,,paying ,a ,,debt4 ,in an office the boy owed one of the clerks threepence1 the clerk owed the cashier twopence1 and the cashier owed the boy twopence4 ,one day the boy1 having a penny1 decided to diminish his debt1 and gave the penny to the clerk1 who in turn paid half his debt by giving it to the cashier1 the latter gave it back to the boy1 saying1 8,that makes one penny ,i owe you now20 the office boy again passed it to the clerk1 who passed it to the cashier1 who in turn passed it back to the boy1 and the boy discharged his entire debt by handing it over to the clerk1 thereby squaring all accounts4 ,a ,,testimonial4 8,how do you like your new typewriter80 inquired the agent4 8,it's grand60 was the immediate and enthusiastic response4 8,i wonder how ,i ever got along without it40 8,well1 would you mind giving me a little testimonial to that effect80 8,certainly not2 do it gladly40 7,a few minutes' pounding74 8,how'll this suit you80 8afted ,using the automatig ,back-action a type writ1 er for thre emonthan d ,over4 ,i unhesittattingly pronounce it prono nce it to be al even more than th e ,manufacturs claim8 for it4 ,during the time been in our possession e4 i4 th ree monthzi id has more th an than paid for itelf in the saving of time an d labrr8 ,john ,gibbs40 ,,state ,,of ,,the ,,poll4 #aai4 ,in a constituency in which each elector may vote for #b candidates half of the constituency vote for ,a1 but divide their votes among ,b1 ,c1 ,d and ,e in the proportion of #d1 #c1 #b1 #a2 half the remainder vote for ,b1 and divide their votes between ,c1 ,d1 ,e in proportion #c1 #a1 #a2 two-thirds of the remainder vote for ,d and ,e1 and #edj do not vote at all4 ,find state of poll1 and number of electors on roll4 #abj4 ,three men1 ,a1 ,b and ,c1 go into an hotel to have a 8free and easy0 on their own account1 and after sundry glasses of ,dewar's ,whisky got into dispute as to who had the most cash1 and neither being willing to show his hand1 the landlord was called upon to umpire4 ,he found that ,a's money and half of ,b's added to one-third of ,c's just came to #cb1 again that one-third of ,a's with one-fourth of ,b's and one-fifth of ,c's made up #ae1 again he found that one-fourth of ,a's together with one-fifth of ,b's and one-sixth of ,c's totalled #ab4 ,how much had each8 ,illustration ,,the ,,bible ,,in ,,schools4 ,,visiting ,,clergyman--8,what's a miracle80 ,,boy--8,dunno40 ,v4,c4--8,well1 if the sun was to shine in the middle of the night what would you say it was80 ,,boy--8,the moon40 ,v4,c4--8,but if you were told that it was the sun1 what would you say it was80 ,,boy--8,a lie40 ,v4,c4--8,i don't tell lies4 ,suppose ,i were to tell you it was the sun1 what would you say then80 ,,boy--8,that you was drunk40 #aba4 ,a man travels #fj miles in #c hours by rail and coach2 if he had gone all the way by rail he would have ended his journey an hour sooner and saved two-fifths of the time he was on the coach4 ,how far did he go by coach8 ,,wanted ,canvasser1 energetic2 only 8live0 men need apply4 ,smart ,co4 ,a determined-looking young man rushed into ,mr4 ,sharp's office the other day1 and1 addressing him1 said abruptly1 8,see you're advertising for a canvasser1 sir2 ,i've come to fill the place40 8,gently1 young man6--gently6 ,how do you know that you'll suit80 asked ,mr4 ,sharp1 somewhat nettled at the young man's off-hand manner4 8,certain of it4 ,best man you could have--energetic1 punctual1 honest1 sober1 ,a#a references1 and----0 8,wait a minute1 ,i tell you60 shouted ,mr4 ,sharp4 8,i don't think you'd suit me at all40 8,oh1 yes1 ,i shall10 said the young man1 seating himself4 8,and ,i don't go out of this office till you engage me40 8,you won't80 yelled ,mr4 ,s4 8,certainly not10 said the young man1 calmly4 8,why1 you impudent young scoundrel6 ,i'll--,i'll kick you out60 8,no1 you wont4 ,you may kick me1 but you won't kick me out40 8,if you don't go1 ,i'll call a policeman10 declared ,mr4 ,s41 purple with rage4 8,will you80 ,the young man rushed to the door1 locked it1 and put the key in his pocket4 ,mr4 ,s4 gasped and glared1 and then roared3-- 8,i tell you ,i won't have you6 ,get out of my office4 ,will you take #8no' for an answer80 8,no1 ,i won't take #8no' for an answer4 ,never did in my life1 and don't intend starting now10 said the young man1 very determinedly4 ,mr4 ,sharp hesitated1 then rose to his feet1 with admiration beaming from his eyes4 8,young man10 he said1 8,i've been looking for an agent like you for twenty years4 ,at first ,i thought you were only a bumptious fool2 but now ,i see you're literally bursting with business4 ,if any man can sell my patent vermin-trap 7warranted to catch anything from a flea to a tiger7 you're that man4 ,a hundred a year and #ae per cent4 commission4 ,is it a bargain80 8,it is10 said the young man1 trying the trap1 and smiling approvingly when it nipped a piece of flesh clean out of his finger4 ,,why ,,is ,,it8 ,take a long narrow strip of paper1 and draw a line with pen or pencil along the whole length of its centre4 ,turn one of the ends round so as to give it a twist1 and then gum the ends together4 ,now take a pair of scissors and cut the circle of paper round along the line1 and you will have two circles4 ,this is a puzzle within a puzzle1 and has never been satisfactorily explained either by scientist or mathematician4 ,how to ,read a ,person's ,character4 ,tell a friend to put down in figures the year in which he was born2 to this add #d1 then his age at last birthday provided it has not come in the present year 7if it has1 then his age last year72 multiply this sum by #ajjj1 and subtract #fhg1dbc4 7,this number is for #ahii2 it increases #ajjj for each succeeding year47 ,to the remainder place corresponding letters of the alphabet4 ,the result will be the popular name by which your friend is known4 ,example3 ,a person was born in #ahfj1 and is now #ch years of age4 #ahfj #d ---- #ahfd #ch ,age ---- #aijb #ajjj -------- #aijbjjj #fhgdbc -------------- #a1b1a1d1e1g1g a1b1a1d1e1g1g 78,a bad egg407 #abb4 ,there are #c numbers in continued proportion--the middle number is #fj1 and the sum of the others is #abe4 ,find the numbers4 #abc4 ,a lends ,b a certain sum at the same time he insures ,b's life for #gcg #abs4 #f;d41 paying annual premiums of #bj2 at the end of three years and just before the fourth premium is to be paid1 ,b dies1 having never repaid anything4 ,what sum must ,a have lent ,b in order that he may have just enough to recoup himself1 together with #e per cent4 compound interest on the sum lent and on the premiums8 #abd4 ,i met three ,dutchmen--,hendrick1 ,claas1 and ,cornelius--with their wives--,gertruig1 ,catrn1 and ,anna2 in answer to a question they told me they had been to market to buy pigs1 and had spent between them #bbd #aas2 ,hendrick bought #bc pigs more than ,catrn1 and ,class bought #aa more than ,gertruig1 each man laid out #c guineas more than his wife4 ,now find out each couple--man and wife4 ,,curious ,,book-,,keeping4 ,an old tradesman used to keep his accounts in a singular manner4 ,he hung up two boots--one on each side of the chimney2 into one of these he put all the money he received1 and into the other all the receipts and vouchers for the money he paid4 ,at the end of the year1 or whenever he wanted to make up his accounts1 he emptied the boots1 and by counting their several and respective contents he was enabled to make a balance1 perhaps with as much regularity and as little trouble as any book-keeper in the country4 ,,quicker ,,than ,,thought4 ,a little boy1 hearing someone remark that nothing was quicker than thought1 said3 8,i know something that is quicker than thought40 8,what is it1 ,johnny80 asked his pa4 8,whistling10 said ,johnny4 8,when ,i was in school yesterday ,i whistled before ,i thought1 and got caned for it1 too40 #abe4 ,the number of men in both fronts of two columns of troops ,a and ,b1 when each consisted of as many ranks as it had men in front1 was #hd2 but when the columns changed ground1 and ,a was drawn up with the front ,b had1 and ,b with the front ,a had2 the number of ranks in both columns was #ia4 ,required3 the number of men in each column4 ,,running ,,through ,,his ,,fortune4 #abf4 ,a man inheriting money spends on the first day #ais41 twice that amount on the next1 and #ais4 additional every day till he exhausts his fortune by spending on the last day #aij by way of having a real good time of it and treating his friends to a good 8blow out40 ,what amount of money had he left to him at the start8 #abg4 ,a shopkeeper makes on a certain article the first day a profit of #c;d41 the second day #db;d41 and so on1 profit increasing each day by #ab;d4 ,he had a profit of #ads4 #c;d4 on the whole4 ,how many days was he selling the article8 8,,awful ,,sacrifice40 ,one of those generous1 disinterested1 self-sacrificing tradesmen1 having stuck upon every other pane of glass in his window1 8,selling-off10 8,no reasonable offer refused10 8,must close on ,saturday10 offered himself as bail1 or security1 in some case which was brought before a magistrate1 when the following dialogue ensued3--,the magistrate asking him if he was worth #bjj1 8,yes10 he replied4 8,but you are about to remove1 are you not80 8,no40 8,why1 you write up1 #8,selling-off4'0 8,yes1 every shopkeeper is selling off40 8,you say1 #8,no reasonable offer will be refused4'0 8,well1 ,i should be very unreasonable if ,i did refuse such offers40 8,but you say1 #8,must close on ,saturday4'0 8,to be sure2 you would not have me open on ,sunday1 would you80 #abh4 ,a man dying left his property of #aj1jjj to his four children1 aged respectively #f1 #h1 #aj1 and #ab years1 on the understanding that each on attaining his majority shall receive the same amount of money1 comp4 interest at the rate of #d per cent4 being allowed4 ,what is the amount of the #aj1jjj payable to each8 ,a ,,waste ,,of ,,time4 ,a little boy spent his first day at school4 8,what did you learn80 was his aunt's question4 8,didn't learn nothing40 8,well1 what did you do80 8,didn't do nothing4 ,there was a woman wanting to know how to spell #8cat1' and ,i told her40 ,an ,english ,school-boy's ,essay on ,australia4 8,part of ,austrailya is vague4 ,it ust to be used by the ,english to keep men on that was not bad enough to be killed4 ,some farms would raise as much as five hundred thousand4 ,the ,english long ago ust to send their prisoners there when they did anything not worth hanging4 8,austrailya is a vast ,country1 and the biggest ,island on the surface of the ,earth4 ,it has all its bad men and they have found a great many ,gold and ,diamonds there1 and ,sidney is one of the ,chief ,countries in it which is in new south ,wales4 8,it used to be used for purposes of ,exploration1 but it has no interior1 and you can't explore it4 ,sometimes it is called ,antipides1 because everything is upside down there4 ,the chief products are ,wool and ,gold and other ,exports and the ,austrailyan eleven come from there4 ,the ,climate is hot in the ,summer and not so in the ,winter1 which causes drowts and sweeps all the sheep away and the banks break4 8,it was discovered by ,captain ,cook who captured it from the ,dutch4 ,there are no wild ,animals there except the ,kangaroo1 they fly through the air with great skill and then they return again right to your feet4 ,the natives are coloured ,black and they call themselves ,aboriginels1 they subsist on bark and other food they do no work and chop wood for a miserable living and can smell the ground like a dog4 ,when we go there they call us new ,chums4 ,they have no form of ,worship1 and pray for rain1 but a belief in ,federashun because they want to be joined together4 8,their only amusement is ,co-robbery4 ,it is celebrated for ,bushrangers and the ,melbourne ,cup which sticks people up and takes from them all they have got4 8,austrailya has a lot of aliasses1 one is new ,holland and afterwards it was called ,pollynesia1 and ,van ,demon and ,oceana but sir ,henry ,parks called it ,austrailya on his ,death-bed4 ,you can go to it in a ship but it is joined to ,great ,britain by a cable40 #abi4 ,i ran to a certain railway station to meet the train which was due at #c4ae p4m4 ,when ,i arrived on the platform the hands of the clock made equal angles with #c o'clock4 ,how long had ,i to wait8 ,illustration #acj4 ,the wall of ,china is #aejj miles long1 #bj feet high1 #ae feet wide at the top and #be at the bottom4 ,the largest of the pyramids is said to have been #gda feet at the base1 #dha feet vertical when finished4 ,how many such pyramids could be built out of the wall of ,china8 ,,grammar4 ,,schoolmaster--8,now1 boys1 the word #8with' is a very bad word to end a sentence with40 #aca4 ,there is an arch of quadrantal form2 the rise of the crown is #ag feet4 ,what is the span8 #acb4 ,two pairs of fives ,i bid you take1 ,and four times four and forty make4 #acc4 ,a lady bought a quantity of flannel1 which she distributed among some poor women2 the first received #b yards1 the second #d yards1 and so on2 the lot cost her #e #ads4 #b;d4 ,how many women were there1 and what did the lady pay per yard8 #acd4 ,a and ,b marry1 their respective ages being in proportion to #c and #d4 ,now after they have been married #ad years their ages are as #e to #f1 and the age of ,a is #e times that of her youngest child1 who was born when the parents' ages were as #d to #e4 ,required3 the ages of ,a and ,b when they were married1 and the age of the youngest child now that they have been married #ad years4 ,,an ,,appalling 8,,sum40 ,at a school1 a short time back1 the pupils were given1 as a home lesson1 the task of subtracting from #hhj1ghh1hhi the number #fbi so often till nothing remained4 ,the boys worked on for hours without any perceptible diminution of the figures1 and at length gave up the task in despair4 ,some of the parents then tried their hands1 with no better success4 ,for1 in order to work out the sum1 the number #fbi would have to be subtracted #a1djj1cjj times1 leaving #ahi as a remainder4 ,working #ab hours a day1 at the rate of #c subtractions per minute1 it would take over #a year and #i months to complete the sum which had been set the poor lads for their home lesson4 ,a ,,military ,,luncheon4 #ace4 ,a certain number of ,volunteers--namely1 ,commissioned ,officers1 ,non-commissioned ,officers1 and ,privates had a dinner bill to pay2 there were1 it seemed1 half as many more ,non-,com4 ,officers as ,com41 one-third as many more ,privates as ,non-,com4 ,officers1 and they agreed that each ,commissioned ,officer should pay one-third as much again as each ,non-,com41 and each ,non-,com4 one-fifth as much again as each ,private2 but #a ,commissioned and #b ,non-,com4 ,officers slipped away without paying their portion 7#es471 each of the others had to pay in consequence #d;d4 more4 ,what was the amount of the bill1 and the number of each present8 ,twice the half of #a8 ,ask your friends--it bothers them4 ,the ,problem ,easily ,solved4 8,do you see that row of poplars on the other bank standing apparently at equal distances apart80 asked a grave-faced man of a group of people standing by a river4 ,the group nodded assent4 8,well1 there's quite a story connected with those trees10 he continued4 8,some years ago there lived in a house overlooking the river a very wealthy banker1 whose only daughter was beloved by a young surveyor4 ,the old man was inclined to question the professional skill of the young rod and level1 and to put him to the test directed him to set out on the river shore a row of trees1 no two of which should be any further apart than any other two4 ,the trial proved the lover's inefficiency1 and forthwith he was forbidden the house1 and in despair drowned himself in the river4 ,perhaps some of you gentlemen with keen eyes can tell me which two trees are furthest apart80 ,the group took a critical view of the situation1 and each member selected a different pair of trees4 ,finally1 after much discussion1 an appeal was made to the solemn-faced stranger to solve the problem4 8,the first and the last10 said he1 calmly1 resuming his cigar and walking away with the air of a sage4 #acf4 ,twice five of us are eight of us1 and two of us are three1 ,and three of us are five of us--now how can all this be8 ,if that does not puzzle you ,i'll tell you one thing more3 ,eight of us are five of us and five of us are four4 8,,expressional0 ,,measures4 ,the table of measures says that #c barleycorns make #a inch--and so they do4 ,when the standards of measures were first established #c barleycorns1 well-dried1 were taken out and laid end to end1 and measured an inch4 ,the 8hairbreadth0 now used indefinitely for infinitesimal space1 was a regular measure1 #af hairs laid side by side equalling #a barleycorn4 ,the expression 8in a trice10 as everyone knows1 means a very short space of time4 ,the hour is divided into #fj minutes1 the minute into #fj seconds1 and the second into #fj 8trices40 ,a ,,challenge4 #acg4 ,a lady belonging to the ,w4,c4,t4,u4 was endeavouring to persuade a gentleman friend of hers to give up the drink2 he replied1 8,i will sign the pledge if you tell me how many glasses of beer did ,i drink to-day if the difference between their number and the number of times the square root of their number is contained in #b be equal to #c40 ,,memory ,,system4 ,,teacher--8,in what year was the battle of ,waterloo fought80 ,,pupil--8,i don't know40 ,,teacher--8,it's simple enough if you only would learn how to cultivate artificial memory4 ,remember the twelve apostles4 ,add half their number to them4 ,that's eighteen4 ,multiply by a hundred4 ,that's eighteen hundred4 ,take the twelve apostles again4 ,add a quarter of their number to them4 ,that's fifteen4 ,add to what you've got4 ,that's #ahae4 ,that's the date4 ,quite simple1 you see1 to remember dates if you will only adopt my system40 ,a ,,globe ,,trotter4 #ach4 ,everyone knows that in a race on a circular track the competitor who has the 8inside0 running has the least ground to cover1 hence the great desire of cyclists1 jockeys1 c41 to 8hug the fence40 ,now a gentleman1 six feet high1 starts walking round the ,earth on the equator2 his feet1 therefore1 have the inside running4 ,find out how much further his head travels than his feet in performing this wonderful journey8 taking the circumference of the globe at the equator to be #be1jjj miles4 ,illustration ,,precocious ,,juvenile--8,mamma1 it isn't good grammar to say #8after ,i1' is it80 ,,his ,,mother--8,no1 ,georgie40 ,,precocious ,,juvenile--8,well1 the letter ,j comes after ,i4 ,which is wrong--the grammar or the alphabet80 #aci4 ,there is an island in the form of a semi-circle2 two persons start from a point in the diameter2 one walks along the diameter1 and the other at right angles to it2 the former reaches the extremity of the diameter after walking #d miles1 and the latter the boundary of the island after walking #h miles4 ,find the area of the island4 #adj4 ,there is a certain number consisting of three figures which is equal to #cf times the sum of its digits1 and #g times the left-hand digit plus #i1 equal to #e times the sum of the remaining digits1 and #h times the second digit minus #i is equal to the sum of the first and third4 ,what is the number8 #ada4 ,a bottle and cork costs #b;d42 the bottle costs #b;d4 more than the cork4 ,what is the price of each8 ,a ,cure for ,big ,words4 ,here is a good story of how a father cured his son of verbal grandiloquence4 ,the boy wrote from college1 using such large words that the father replied with the following letter3--8,in promulgating your esoteric cogitations1 or articulating superficial sentimentalities1 and philosophical or pscyhological observations1 beware of platitudinous ponderosity4 ,let your conversation possess a clarified conciseness1 compacted comprehensibleness1 coalescent consistency1 and a concatenated cogency4 ,eschew all conglomerations of flatulent garrulity1 jejune babblement1 and asinine affectations4 ,let your extemporaneous descantings and unpremeditated expatiations have intelligibility1 without rhodomontade or thrasonical bombast4 ,sedulously avoid all polysyllabical profundity1 pompous prolixity1 and ventriloquial vapidity4 ,shun double entendre and prurient jocosity1 whether obscure or apparent4 ,in other words1 speak truthfully1 naturally1 clearly1 purely1 but do not use big words40 #adb4 ,with a pair each of four different weights1 #a lb4 up to #agj lbs4 can be weighed4 ,what are the weights8 #adc4 ,a man going 8on the spree0 spends on the first day #ajs4 #e;d41 the second #ahs41 the third #a #hs4 #g;d41 the fourth #b #bs4 #h;d41 and so on at that rate of increase until he has spent all he had--#ahc #fs4 #h;d4 ,how many days was he on the spree8 #add4 ,divide one shilling into two parts1 so that one will be #b;d4 more than the other4 ,,complimentary1 ,,very6 ,,editor--8,did you see the notice ,i gave you yesterday80 ,,shopkeeper--8,yes1 and ,i don't want another4 ,the man who says ,i've got plenty of grit1 and that the milk ,i sell is of the first water1 and that my butter is the strongest in the market1 may mean well1 but he is not the man whose encomiums ,i value40 #ade4 ,a vintner draws a certain quantity of wine out of a full vessel that holds #bef gallons1 and then filling the same vessel with water draws off the same quantity of liquor as before1 and so on for four draughts1 when only #ha gallons of pure wine is left4 ,how much wine did he draw each time8 #adf4 ,a man has #d horses1 for which he gave #hj2 the first horse cost as much as the second and half of the third1 the second cost as much as the fourth minus the cost of the third1 the third cost one-third of the first1 and the fourth cost as much as the second and third together4 ,what was the price of each horse8 ,the ,divided ,pound4 #adg4 ,a father wishes to divide #a between his four sons1 giving one-third to one1 one-fourth to another1 one-fifth to another1 and one-sixth to another2 in doing so he finds he has only disbursed #ais42 the balance1 #as41 is then divided in the same proportion4 ,what amount does each receive in full in the proportion named8 ,,railway-,,shunting ,,puzzle4 #adh4 ,a locomotive is on the main line of railway2 the trucks marked #a and #b are on sidings which meet at the points1 where there is room for one truck only and not for the locomotive4 ,it is desired to reverse the position of the trucks--that is1 put #a where #b is1 and #b where #a is1 and yet leave the locomotive free on the main line4 ,this must be done by means of the locomotive only1 either pulling or pushing the trucks--it may be between them1 thus pulling one and pushing the other--but no truck must move without the locomotive4 ,illustration ,in working this puzzle out1 it would be best to draw the diagram on an enlarged scale1 and have articles to represent the trucks and locomotive4 #adi4 ,in a public square there is a fountain containing a quantity of water2 around it stand a group of people with pitchers and buckets4 ,they draw water at the following rate3 ,the first draws #ajj quarts and one-thirteenth of the remainder1 the second #bjj quarts and one-thirteenth of the remainder1 the third #cjj quarts and one-thirteenth1 and so on1 until the fountain was emptied4 ,how many quarts were there in the fountain8 ,,english ,,from ,a ,,german ,,master4 ,,prof4 ,,goldburgmann--8,herr ,kannstnicht1 you will the declensions give in the sentence1 8,i have a gold mine40 ,,herr ,,kannstnicht--8,i have a gold mine2 thou hast a gold thine2 he has a gold his2 we1 you1 they have a gold ours1 yours1 or theirs1 as the case may be40 ,,prof4 ,,goldburgmann--8,you right are2 up head proceed4 ,should ,i what a time pleasant have if all ,herr ,kannstnicht like were60 ,,spending ,,their 8,,all40 #aej4 ,three men going 8on the spree0 decide to spend all their money4 ,the first1 ,a1 8shouts0 for the company and then gives his balance to ,b1 who also in turn pays for #c drinks and gives his balance to ,c1 who can then just manage to pay for drinks once more at #f;d4 each4 ,how much money had each8 #aea4 ,there is a regiment of #gcjj soldiers1 which is to be divided into #d companies--half of the first company1 two-thirds of the second1 three-quarters of the third1 and four-fifths of the fourth--to be composed of the same number of men4 ,how many soldiers are there in each company8 ,a ,,grave ,,mistake4 ,a ,scotch tradesman1 who had amassed1 as he believed1 #djjj1 was surprised at his old clerk's showing by a balance-sheet his fortune to be #fjjj4 8,it canna be--count again10 said the old man4 ,the clerk did count again1 and again declared the balance to be #fjjj4 ,time after time he cast up the columns--it was still a #f1 and not a #d1 that rewarded his labours4 ,so the old merchant1 on the strength of his good fortune1 modernised his house1 and put money in the purse of the carpenter1 the painter1 and the upholsterer4 ,still1 however1 he had a lurking doubt of the existence of the extra #bjjj2 so one winter's night he sat down to give the columns 8one count more40 ,at the close of his task he jumped up as though he had been galvanised1 and rushed out in a shower of rain to the house of the clerk1 who1 capped and drowsy1 put out his head from an attic window at the sound of the knocker1 mumbling1 8,who's there1 and what d'ye want80 8,it's me1 ye scoundrel60 exclaimed his employer4 8,ye've added up the year of our ,lord amang the poons60 ,,problem ,,for ,,printers4 #aeb4 ,a book is printed in such a manner that each page contains a certain number of lines1 and each line a certain number of letters4 ,if each page contains #c lines more1 and each line #d letters more1 the number of letters in each page will be #bbd more than before2 but if each page contains #b lines less1 and each line #c letters less1 the number of letters in each page would be #ade less than before4 ,find the number of lines in each page1 and the number of letters in each line4 ,,the ,,income ,,tax4 #aec4 ,the charge on a major income is the same in amount as that on a minor one1 which is #b per cent4 of their mutual difference1 but the rate imposed on the overplus of a major income is #d per cent41 so that on a composite income of the major and minor the charge would be #c #hs4 ,required the major and minor incomes4 8,your ,money or ,your ,life60 #aed4 ,two gentlemen1 ,a and ,b1 with #ajj and #dh respectively1 having to perform a long journey through a lonely part of the country1 agree to travel together for purposes of safety2 they are1 however1 taken unawares by a gang of bushrangers who1 calling upon them to 8bail up10 ease them of some of their cash4 ,the leader of the gang was satisfied with taking twice as much from ,a as from ,b1 and left to ,a three times as much as to ,b4 ,how much was taken from each8 ,illustration ,,geometrical ,,music4 ,a point1 my boys1 is that which has no length1 breadth1 or dimension4 -- ,a line has length1 and yet is but a point drawn in extension4 ,all lines have names expressing some distinguishing particular4 ,as3 horizontal1 parallel1 oblique1 and perpendicular4 ,chorus of ,pupils4 ,oh6 dear6 oh6 ,a pretty science mathematics is to know4 ,the lines called parallel are those which1 drawn in one direction1 ,continued to infinity1 will never make bisection4 ,the thing perhaps sounds odd1 but if you entertain a doubt1 boys1 ,i'll draw the lines1 now take your slates1 and work the problem out1 boys4 ,chorus of ,pupils4 ,oh6 dear6 no6 ,we readily believe it1 ,sir6 since you say so6 #aee4 ,in this figure rub out eight lines1 and leave two squares4 ,no side nor angle of any square must be left1 otherwise that will be counted as a square4 ,illustration #aef4 ,a and ,b travelled by the same road1 and at the same rate from ,tamworth to ,sydney4 ,a overtook a flock of sheep1 which travelled at the rate of three miles in two hours1 and two hours after he met a mail coach1 which travelled at the rate of nine miles in four hours4 ,b overtook the flock #de miles from ,sydney1 and met the coach #dj minutes before he came to the #ca-mile post from the ,metropolis4 ,where was ,b when ,a reached ,sydney8 ,,english ,,history4 ,a school examination paper contained the question3--8,write down all you know about ,henry ,,viii10 and one of the small boys answered as follows3-- 8,king ,henry #h was the greatest widower that ever lived4 ,he was born at ,anne ,domini in the year #ajff4 ,he had #eaj wives besides children4 ,the first was beheaded and afterwards executed1 and the second was revoked4 ,she never smiled again4 ,but she said the word #8,calais' would be found on her heart after death4 ,the greatest man in this reign was ,lord ,sir ,garret ,wolsey--named the ,boy ,bachelor4 ,he was born at the age of fifteen unmarried4 ,henry #h was succeeded on the throne by his great-grandmother1 the beautiful ,mary1 ,queen of ,scots1 sometimes called ,lady of the ,lake or the ,lay of the ,last ,minstrel40 #aeg4 ,two boys1 ,a and ,b1 run round a ring in opposite directions till they meet at the starting point1 their last meeting place before this having been #iij yards from it4 ,if ,a's rate to ,b's be as #e to #c1 find the distance they have travelled4 ,,the ,,value ,,of ,,home ,,lessons4 ,two teachers of languages were discussing matters and things relative to their profession4 8,do your pupils pay up regularly on the first of each month80 asked one of them4 8,no1 they do not10 was the reply2 8,i often have to wait weeks and weeks before ,i get my pay1 and sometimes ,i don't get it at all4 ,you can't well dun the parents for the money40 8,why don't you do as ,i do8 ,i always get my money regularly40 8,how do you manage it80 8,it is very simple4 ,for instance1 ,i am teaching a boy ,french1 and on the first day of the month his folks don't send the amount due for the previous month4 ,in that case ,i give the boy the following exercise to translate and write out at home3--#8,i have no money4 ,the month is up4 ,hast thou any money8 ,have not thy parents any money8 ,i need money very much4 ,why hast thou brought no money this morning8 ,did thy father not give thee any money8 ,has he no money in the pocket-book of his uncle's great aunt8' ,this fetches them4 ,next morning that boy brings the money40 #aeh4 ,there is a number half of which divided by #f1 one-third of it divided by #d1 and one-fourth of it divided by #c1 each quotient will be #i4 ,what is the number8 ,,quibble4 #aei4 ,two-thirds of six is nine1 one-half of twelve is seven1 ,the half of five is four1 and six is half of eleven4 ,,something ,,easy4 #afj4 ,find a sum of s4 d4 7no farthings7 in which the figures1 in their order1 represent the amount reduced to farthings4 #afa4 ,three persons won a 8consultation0 worth #a1cbj4 ,if ,j were to take #f1 ,m ought to take #d1 and ,b #b4 ,what is each person's share8 8,,on ,,the ,,job40 #afb4 ,six masons1 four bricklayers and five labourers were working together at a building1 but being obliged to leave off one day by the rain1 they went to a public-house and drank to the value of #des41 which was paid by each party in the following manner3 ,four-fifths of what the bricklayers paid was equal to three-fifths of what the masons paid1 and the labourers paid two-sevenths of what the masons and bricklayers paid4 ,what did each party of men pay8 ,illustration #afc4 ,in a certain speculation ,i gained #d #ais4 #aa;d4 for each pound ,i expended1 and by a curious coincidence ,i found that #d #ais4 #aa;d4 was the exact amount ,i had ventured4 ,required the amount of capital and profit together4 ,,his ,,majority4 #afd4 8,i am not a man1 ,i suppose1 till ,i am #ba4 ,how long have ,i to wait yet1 if the cube root of my age eight years hence1 added to the cube root of my age eleven years ago would make #e80 ,,draught-,,board ,,puzzle4 #afe4 ,place eight men on a draught-board in such a way that no two will be in a line either crossways or diagonally4 ,of course the two colours on the board must be used4 #aff4 ,a gentleman1 dying1 left his property thus3 ,to his wife1 three-fifths of his son's and youngest daughter's shares2 to his son1 four-fifths of his wife's and eldest daughter's shares2 to his eldest daughter1 two-sevenths of his wife's and son's shares1 and to his youngest daughter one-sixth of his son's and eldest daughter's shares4 ,the wife's share was #d1fej4 ,what did the gentleman leave1 and what did each receive8 ,,samson ,,outdone4 ,a man boasted that he carried off an entire timber yard in his left hand4 ,it turned out that the timber-yard was a three-foot rule4 ,domino ,puzzle4 ,illustration #afg4 ,arrange the #bh dominoes in such a manner as to have two squares of each number2 there are eight half-squares of each number in the complete set--eight sixes1 eight fives1 c4--so that four of the one number comprise a square4 ,the whole1 when finished1 will form a figure like a square1 resembling a wide letter ,i4 ,illustration #afh4 ,a sum of money is divided among a number of persons2 the second gets #h;d4 more than the first1 the third gets #as4 #d;d4 more than the second1 the fourth #bs4 more than the third1 and so on4 ,if the first gets #f;d4 and the last #e #bs4 #f;d41 how many persons were there8 ,,it ,,couldn',t ,,be ,,expected4 ,teacher3 8,johnny1 where is the ,north ,pole80 ,johnny3 8,i don't know40 ,teacher3 8,don't know where the ,north ,pole is80 ,johnny3 8,when ,franklin1 ,nansen and ,captain ,andre hunted for it and couldn't find it1 how am ,i to know where it is80 #afi4 ,for a loan of #b1ejj1jjj1 #d per cent4 per annum is paid by a mining company whose capital is #d1ijj1jjj4 ,the working expenses constitute #eb per cent4 of the gross receipts1 which amount in the year to #ife1jjj1 and the directors set apart #dd1dej as a reserve fund4 ,what yearly dividend do the shareholders receive8 #agj4 ,if a monkey climbs a greasy pole #aj ft4 high1 ascending #a ft4 with each movement of his arms1 and slipping back #f in4 after each advance2 how many movements would he have to make1 to touch the top1 and what height would he have climbed in all8 #aga4 ,find two numbers whose ,g4,c4,m4 is #agi1 ,l4,c4,m4 #efche1 and difference #ajchb4 #agb4 ,what is the difference between twenty four-quart bottles1 and four and twenty quart bottles8 ,,the ,g4,c4,m4 ,the ,greatest ,common ,measure--,a 8long pint40 #agc4 ,there are two casks1 one of which holds thirty gallons more than the other4 ,the larger is filled with wine1 the smaller with water4 ,ten gallons are taken out of each3 that from the first is poured into the second2 the operation is repeated1 and it is now found that the larger cask contains #ac gallons of water4 ,find the contents of each cask4 #agd4 ,in the midst of a paddock well stored with grass1 ,i engaged just an acre to tether my ass2 ,what length must that cord be1 in grazing all round ,that he may graze over just one acre of ground8 #age4 ,if three first-class cost as much as five second-class tickets for a journey of #ajj miles1 the total cost of the eight tickets being #c #bs4 #f;d41 find the charge per mile for each first-class and second-class ticket4 ,,humility4 ,in a certain street are three tailors4 ,the first to set up shop hung out this sign--8,here is the best tailor in the town40 ,the next put up--8,here is the best tailor in the world40 ,the third simply had this--8,here is the best tailor in this street40 8,on the ,wallaby40 #agf4 ,four sundowners called at a station and asked for rations4 8,well10 said the manager1 8,i have a job that will take #bjj hours to complete2 if you want to do it1 you can divide the work and the money among yourselves as you see fit40 ,the sundowners agreed to do the work on these conditions4 8,now1 mates10 said the laziest of them1 8it's no good all of us doing the same amount of work4 ,let's toss up to see who shall work the most hours a day1 and who the fewest4 ,then let each man work as many days as he does hours a day40 ,this was agreed to2 but the proposer took good care that chance should designate him to do the least number of hours of work4 ,how were the #bjj hours put in so that each man should work as many hours as days1 and yet no two men work the same number of hours8 #agg4 ,on multiplying a certain number by #eag a result is obtained greater by #g1cjc1ece than if the same number had been multiplied by #cab4 ,how much greater still would be the result if #haa were the multiplier instead of #cab8 ,a 8,,catch40 #agh4 ,six ears of corn are in a hollow stump4 ,how long will it take a squirrel to carry them all out if he takes but three ears a day8 ,,number #g4 ,the number #g has always been considered the most sacred of all our figures4 ,its prominence in the ,scriptures is very remarkable1 from ,genesis--where we read that the seventh day was consecrated as a day of rest and repose--to ,revelations--where we find the seven churches of ,asia2 seven golden candlesticks2 the book with seven seals2 the seven angels with seven trumpets2 seven kings2 seven thunders2 seven plagues1 c41 c41 its frequent occurrence is most striking4 ,the ,ancients paid great respect to the seven mouths of the ,nile4 ,the seven rivers of ,vedic ,india2 seven wonders of the world2 seven precious stones2 seven notes of music2 seven colours of the rainbow1 c41 c4 ,the 8,lampads seven that watch the ,throne of ,heaven0 led the ,chaldeans to esteem the unit #g as the holiest of all numbers1 thereupon they established the week of seven days1 and built their temples in seven stages4 ,the temples and palaces of ,burma and ,china are seven-roofed4 ,in modern times this number has kept up its reputation4 ,shakespeare paid special regard to it2 the 8seven ages0 and every multiple of it is supposed to be a critical or important period in one's life4 ,a modern philosopher as follows apportions-- ,,man',s ,,full ,,extreme4 #g years in childhood1 sport and play1 7#g7 #g years in school from day to day1 7#ad7 #g years at trade or college life1 7#ba7 #g years to find a place and wife1 7#bh7 #g years to pleasure's follies given1 7#ce7 #g years to business hardly driven1 7#db7 #g years for some wild-goose chase1 7#di7 #g years for wealth1 a bootless race1 7#ef7 #g years of hoarding for your heir1 7#fc7 #g years in weakness spent and care1 7#gj7 ,and then you die and go--you know not where4 ,very many superstitious and curious ideas have been and still are connected with all our figures4 ,for those interested in this subject see page #adf--8;,how ,to ,become ,quick ,at ,figures0 7,student's ,edition74 8,what's the difference10 asked a teacher in arithmetic1 8between one yard and two yards80 8,a fence10 said ,tommy ,yates4 ,then ,tommy sat on the ruler #ad times4 #agi4 ,what relation is a woman to me who is my mother's only child's wife's daughter8 ,,the ,,advantages ,,of ,,skilful ,,book-,,keeping4 ,if a merchant wishes to get pretty deeply in debt1 and then get rid of his liabilities by bankruptcy--if1 in fact1 he proposes to himself to go systematically into the swindling business1 and engage in wholesale pecuniary transactions without a shilling of his own1 the first thing he should take care to learn would be the whole art of book-keeping4 ,from what may occasionally be seen of the reports of the proceedings in bankruptcy1 it is found that well kept books are regarded as quite a test of honesty1 and though assets may have disappeared or never have existed1 though large liabilities may have been incurred without any prospect of payment1 the bankrupt will be complimented on the straight look of his dealings1 if he has shown himself a good book-keeper4 ,to common apprehension it would seem that well kept books would only help to show a reckless trader the ruinous result of his proceedings1 and that while the man without books might flatter himself that all would come out right at last1 the man with exact accounts would only get into hot water with his eyes open4 ,if a man may trade on the capital of others without any of his own1 and get excused on the ground that he has kept his books correctly1 it is difficult to see why a thief who steals purses1 c41 may not plead in mitigation of punishment that he has carefully booked the whole of his transactions4 ,it would be interesting to know the effect of producing a ledger on a trial for felony1 as well as curious to observe whether a burglar would be leniently dealt with on the ground that his house-breaking accounts gave proof of his experience in the science of 8double-entry40 ,therefore it would be well for those interested to procure copies of 8,,re ,,accounts0 and 8,,advanced ,,thought ,,on ,,accounts40 ,,the ,,firm ,,he ,,represented4 ,a commercial traveller handed a merchant upon whom he had called a portrait of his sweetheart in mistake for his business card1 saying that he represented that establishment4 ,the merchant examined it carefully1 remarked that it was a fine establishment1 and returned it to the astonished and blushing traveller with the hope that he would soon be admitted into partnership4 #ahj4 ,a man and a boy being paid for certain days' work1 the man received #bgs41 and the boy1 who had been absent #c days out of the time1 received #abs4 ,had the man1 instead of the boy1 been absent the #c days they would both have claimed an equal sum4 ,find out the wages of each per day4 #aha4 ,the extremes of an arithmetical series are #ba and #dig1 and the number of terms is #da4 ,what is the common difference8 #ahb4 ,a wine which contains #g per cent4 of spirit is frozen1 and the ice which contains no spirit being removed the proportion of spirit in the wine is increased by #h per cent4 ,how much water in the shape of ice was removed from #ejd gallons of the mixture8 ,,the ,,sharp ,,selector4 #ahc4 ,a selector rented a farm1 and agreed to give his landlord two-fifths of the produce1 but prior to the time of dividing the corn the selector used #de bushels4 ,when the general division was made it was proposed to give to the landlord #ah bushels from the heap in lieu of the share of the #de bushels which the tenant had used1 and then to begin and divide the remainder as though none had been used4 ,would this method have been correct8 ,a ,,good 8,,ad40 ,a member of a certain firm appeared in a law court with a complaint that his partner would sell goods at less than cost price1 and he desired to have him restrained4 ,the defendant utterly denied the charge1 and the case was adjourned for a fortnight4 ,as the plaintiff went out of court he exclaimed in a tragic tone3 8,then the sacrifice must still go on60 and 8,i'll be ruined60 ,the story was noised abroad1 and the result was that the shop was besieged by customers every day4 ,there the case ended1 for at the end of the fortnight the plaintiff failed to appear in court1 having accomplished his purpose--advertisement4 #ahd4 ,i give #c sovereigns for #b dozen wine at different rates per dozen1 and by selling the cheaper kind at a profit of #ae per cent4 and the dearer at a loss of #h per cent4 ,i obtain a uniform price for both4 ,what did each dozen cost me8 #ahe4 ,i have in my garden a shrub that grows #ab inches every day1 but during the night it withers off to half the height that it was at the end of the previous day4 ,how much short of #b feet will it be at the end of a year8 ,,tit-,,for-,,tat4 #ahf4 ,a farmer puts a #c lb4 stone in a keg of butter worth #aa;d4 a pound4 ,the merchant cheats him out of #a lb4 on the weight1 and then does him out of #as4 #aa;d4 on calico1 tobacco1 and a shovel4 ,who is ahead1 and how much8 #ahg4 ,trains leave ,london and ,edinburgh 7#djj miles apart7 at the same time and meet after #e hours2 the train which leaves ,london travels #h miles an hour faster than that which leaves ,edinburgh4 ,at what rate did the former travel1 and at what speed must the latter travel after they have met1 in order that they both may reach their destinations at the same time8 8,,good ,,enough60 8,will you give me a glass of beer1 please80 asked a rather seedy-looking fellow with an old but well-brushed coat and almost too shiny a hat4 ,it was produced by the barmaid1 frothing over the edge of the tumbler4 8,thank you10 said the recipient1 as he placed it to his lips4 ,having finished it in a swallow1 he smacked his lips and said1 8,that is very good beer--very6 ,whose is it80 8,why1 that ,perkins's----0 8,ah6 ,perkins's1 is it6 ,well1 give us another glass40 ,it was done2 and holding it up to the light and looking through it1 the connoisseur said3-- 8',pon my word1 it is grand beer--clear as ,madeira6 ,what a fine color6 ,i must have some more of that2 give me another glass40 ,the glass was filled again1 but before putting it to his lips the imbiber said3-- 8,whose beer did you say this was80 8,perkins's10 emphatically replied the barmaid4 ,the contents of the glass was exhausted1 as also the vocabulary of praise1 and it only remained for the appreciative gentleman to say1 as he wiped his mouth and went towards the door3-- 8,perkins's beer1 is it6 ,i know ,perkins very well2 ,i shall see him soon1 and will settle with him for three long glasses of his incomparable brew4 ,good morning40 ,a ,conspiracy4 #ahh4 ,three gentlemen are going over a ferry with their three servants1 who conspire to rob them if they can get one gentleman to two of them1 or two to three1 on either side of the ferry4 ,they have a boat that will only carry two at once1 and either a gentleman or a servant must bring back the boat each time a cargo of them goes over4 ,how can the gentlemen get over with all their servants so as to avoid an attack8 #ahi4 ,find two numbers whose product is equal to the difference of their squares1 and the sum of their squares equal to the difference of their cubes8 #aij4 ,divide #adjj into such parts as shall have the same ratio as the cubes of the first four natural numbers4 ,this was the tempting notice lately exhibited in the window of a dealer in cheap shirts3 8,they won't last long at this price60 ,,posting ,,the ,,ledger4 ,the well known author of several works on account-keeping1 ,mr4 ,yaldwyn1 tells a rather good thing which actually occurred in ,new ,zealand some time back4 ,mr4 ,yaldwyn was at the time engaged examining the books in one of the offices in a country town1 and enquired from one of the clerks standing near if the ledger were posted4 ,the person appealed to answered that 8he didn't know10 whereupon ,mr4 ,y4 said that he required it done1 and with as little delay as possible4 ,a few minutes later the same individual came rushing in and informed him that the ledger was 8posted40 ,such a piece of 8lightning book-keeping0 so surprised ,mr4 ,y4 that he further questioned the man1 who replied 8,you said you wanted the ledger posted1 and1 begorra1 ,i posted it40 ,it then dawned upon ,mr4 ,yaldwyn that the clerk1 who was an ,irishman1 had actually posted the book in the post office6 ,,they ,,managed ,,it4 ,illustration #aia4 ,billy and ,tommy1 two aboriginals1 killed a kangaroo in the bush1 and began quarrelling over the weight of the animal4 ,they had no proper means of weighing it1 but1 knowing their own weights1 ,billy #acj lbs4 and ,tommy #aij lbs41 they placed a log of wood across a stump so that it balanced with one on each end4 ,they then exchanged places1 and1 the lighter man taking the kangaroo on his knees1 the log again balanced4 ,what was the weight of the kangaroo8 #aib4 ,a son asked his father how old he was1 and received the following answer3 8,your age is now one quarter of mine1 but five years ago it was only one-fifth40 ,how old is the father8 #aic4 ,place three sixes together so as to make seven4 ,,the ,,passing ,,trains ,,puzzle4 #aid4 ,if through passenger trains running to and from ,new ,york and ,san ,francisco daily start at the same hour from each place 7difference of longitude not being considered7 and take the same time--seven days--for the trip1 how many such trains coming in an opposite direction will a train leaving ,new ,york meet before it arrives at ,san ,francisco8 ,,the ,,school-,,teacher 8,,caught40 ,two of our ,public ,schools were engaged playing a football match one afternoon4 ,the head master of one of them had generously given the boys a half-holiday2 but the gentleman who held the same capacity in the other school1 not being an ardent admirer of ,australia's national game1 refused to do so4 ,when school assembled in the afternoon1 a boy volunteered to ask the master for the desired holiday4 ,when the question was put1 he firmly answered1 8,no1 no60 whereupon the bright youth called out3 8,hurrah6 we have our holiday2 two negatives make an affirmative40 ,the teacher was so pleased at the boy's sharpness that he dismissed the school right away4 #aie4 ,a man arrives at the railway station nearest to his home #a hours before the time at which he had ordered his carriage to meet him4 ,he sets out at once to walk at the rate of four miles an hour1 and1 meeting his carriage when it had travelled eight miles1 reaches home exactly one hour earlier than he had originally expected4 ,how far was his house from the station1 and at what rate was his carriage driven8 8,,off ,,the ,,track40 #aif4 ,a man starts to walk from a town1 ,a1 to a town ,b1 a distance by road of #af miles1 at the rate of #d miles an hour4 ,there is a point ,c on the road1 at which the road to ,b leads away to the right1 and another road at right-angles to this latter goes to the left1 8to no place in particular40 ,the unwary traveller gets on to this left hand road1 and is walking for #b hours since he left ,a1 before he finds out his mistake1 and he resolves not to go back to the junction1 which is five miles away1 but makes straight across the bush to ,b1 and strikes it exactly4 ,how long did it take to go from ,a to ,b8 ,,gambling4 #aig4 ,three friends1 ,a1 ,b1 and ,c1 sit down to play cards4 ,as a result of the first game1 ,a lost to each of ,b and ,c as much money as they started to play with2 the result of the second game ,b lost similarly to each of ,a and ,c2 and in the third1 ,c lost similarly to each of ,a and ,b2--and they then had #bds4 each4 ,what had they each at first8 ,this ,sticks ,them ,up4 ,illustration #aih4 ,a1 who is a dealer in horses1 sells one to ,b for #ee4 ,b very soon discovers that he does not require the animal1 and sells him back to ,a for #ej4 ,now1 ,a is not long in finding another customer for the horse3 he sells it to ,c for #fj4 ,how much money does ,a make out of this transaction8 ,this question has been the cause of endless discussion and argument4 ,it might be as well to state that when ,a first sold the horse to ,b he neither made nor lost any money by the deal4 ,,scriptural ,,finance4 #aii4 ,what is the earliest banking transaction mentioned in the ,bible8 ,the answer generally given to this is1 8,the check which ,pharaoh received on the banks of the ,red ,sea1 crossed by ,moses ,co40 ,there is still an earlier instance3 see if you can find it out4 #bjj4 ,how much tea at #fs4 per lb4 must be mixed with #ab lbs4 at #cs4 #h;d4 per lb4 so that the mixture may be worth #ds4 #d;d4 per lb48 #bja4 ,place #ag little sticks--matches1 for instance--making six equal squares1 as in the margin1 then remove five sticks and leave three perfect squares of the same size4 ,illustration ,,for ,,the ,,jeweller4 #bjb4 ,how much gold of #ba and #bc carats must be mixed with #cj oz of #bj carats1 so that the mixture may be #bb carats8 ,,london ,,grammar4 ,three cockneys1 being out one evening in a dense fog1 came up to a building that they thus described4 ,the first said1 8,there's a nouse40 8,no10 said the second1 8,it's a nut40 ,the third exclaimed 8,you're both wrong2 it's a nin60 #bjc4 ,a draper sold #ab yards of cloth at #bjs4 per yard1 and lost #aj per cent4 ,what was the prime cost8 #bjd4 ,a jockey1 on a horse galloping at the rate of #ah miles an hour on the ,flemington racecourse1 passes in #cj minutes over the diameter and curve of a semi-circle4 ,what area does he enclose by the ride8 #bje4 ,how many trees #bj feet apart cover an acre8 8,multiplication is vexation1 ,division is as bad4 ,the rule of three1 it puzzles me1 ,and fractions drive me mad40 ,,multiply #ai #ais4 #aa;d4 ,,by #ai #ais4 #aa;d4 ,this very old question is continually cropping up1 and will continue to do so as long as men are able to reckon4 ,the answer generally given is #cii #ais4 #b;d4 and a fraction1 and the method of working it out as follows3-- #ai #ais4 #aa;d4 #aiaii farthings4 #aiaii #aiaii #cfhfjafja ----- x ----- --------- and so on4 #ifj #ifj #ibafjj ,many adopt the following method3-- #bj x #bj #djj s d #djj #j #j d x d #a_/af less #a_/af ---------------- #cii #ai #aa-ae_/af ,ans4 ,it would be possible to adopt other methods1 each of which would give a different result4 ,properly speaking1 this sum cannot be done4 ,multiplication is merely a contracted form of addition3 it means taking a number or quantity a certain number of times4 ,every multiplication can be proved by addition4 ,all numbers are abstract or concrete--#c is abstract1 #c is concrete4 ,two abstract numbers can be multiplied together--as1 #d times #c #ab4 ,proof3 #c #c #c #c -- #ab ,one abstract number and one concrete number can be multiplied together--as #bs4 multiplied by #c #fs4 ,proof3 #bs4 #bs4 #bs4 --- #fs4 ,two concrete numbers cannot be multiplied together4 ,in the example just given1 #bs4 multiplied by #c1 we see it simply means to write down #bs4 three times1 and by addition we discover the answer to be #fs4 ,suppose the reader lent a friend #bs4 on ,monday1 #bs4 on ,tuesday1 and #bs4 on ,wednesday1 he has lent #bs4 three times1 making #fs4 lent in all4 ,now1 we will attempt to multiply #bs4 by #cs41 but it is impossible to comprehend how many times is #cs4 times4 ,the answer to #bs4 x #cs4 usually given is #fs4 ,on the same lines1 we multiply #i;d4 by #aj;d41 and our answer is--#ij;d41 that is #gs4 #f;d4--a greater product than #bs4 multiplied by #cs4 ,although it is stated that two concrete numbers cannot be multiplied together1 it should be borne in mind that we can multiply yards1 feet1 and inches1 by yards1 feet1 and inches 7length by breadth71 which will result in square or cubic measure3 #ab inches make #a foot1 and #c feet make one yard1 #add square inches make #a square foot1 c4 #ab pence make #a shilling1 but how many square pence make #a square shilling8 ,the argument generally brought forward in favour of the performance of this problem is1 that when the ,rule of ,three is applied to financial questions 7such as interests1 c47 money is multiplied by money4 ,example4--,if the interest on #aj is #aes41 what is the interest on #bj8 ,as #aj 3 #bj 33 #aes4 3 x #ae #aj7cjj ---- #cj ,ans4 #cjs4 ,the multiplication in the above is in appearance only1 for all we get in the ,rule of ,three is the ratio between the sums of money and this ratio is an abstract number1 and not concrete4 ,on examination we find the ratio between #aj and #bj2 that the latter is double1 or two times as much as the former1 and not #b times more than it4 ,we extend a general invitation to all our readers who hold a different opinion to multiply three pints of ,dewar's ,whisky by #f quarts of soda-water1 but in case they might plead inability to perform this little feat1 on conscientious grounds1 we will extend the invitation to three cups of tea by six spoonfuls of sugar4 ,and if any of them have a few pounds 7say #aj7 in the ,savings ,bank we would advise 8,don't add any more deposits1 but wait till you have #b1 then proceed to the bank and multiply the #aj by the #b1 and prove to the teller that you have #bj to your account4 ,be careful to take no less a sum than #b1 or the result might be a little surprising1 for if you take only #a1 the teller might argue after he has received your sovereign that 8ten ones are ten10 and then your #aj would remain the same40 #bjf4 ,what is the difference between six dozen dozen and half a dozen dozen8 ,a ,,tell-,,tale ,,table4 ,there is a good deal of amusement in the following table4 ,it will enable you to tell how old the young ladies are4 ,ask a young lady to tell you in which column or columns her age is found1 add together the figures at the top of the columns in which she says her age is1 and you have the secret4 ,suppose a young lady is #ai4 ,you will find that number in the first1 second and fifth columns2 add the first figures of these columns--#a1 #b and #af--;and you get the age4 #a #b #d #h #af #cb #c #c #e #i #ag #cc #e #f #f #aj #ah #cd #g #g #g #aa #ai #ce #i #aj #ab #ab #bj #cf #aa #aa #ac #ac #ba #cg #ac #ad #ad #ad #bb #ch #ae #ae #ae #ae #bc #ci #ag #ah #bj #bd #bd #dj #ai #ai #ba #be #be #da #ba #bb #bb #bf #bf #db #bc #bc #bc #bg #bg #dc #be #bf #bh #bh #bh #dd #bg #bg #bi #bi #bi #de #bi #cj #cj #cj #cj #df #ca #ca #ca #ca #ca #dg #cc #cd #cf #dj #dh #dh #ce #ce #cg #da #di #di #cg #ch #ch #db #ej #ej #ci #ci #ci #dc #ea #ea #da #db #dd #dd #eb #eb #dc #dc #de #de #ec #ec #de #df #df #df #ed #ed #dg #dg #dg #dg #ee #ee #di #ej #eb #ef #ef #ef #ea #ea #ec #eg #eg #eg #ec #ed #ed #eh #eh #eh #ee #ee #ee #ei #ei #ei #eg #eh #fj #fj #fj #fj #ei #ei #fa #fa #fa #fa #fa #fb #fb #fb #fb #fb #fc #fc #fc #fc #fc #fc ,,coin ,,puzzle4 ,illustration3 #b_/-a;d4 #b_/-a;d4 #b_/-a;d4 #b_/-a;d4 #bjg4 ,place four florins alternately with four pennies1 and in four moves1 moving two adjacent coins each time1 bring the florins together and the pence together4 ,when finished there must be no spaces between the coins4 #bjh4 ,if #b be added to the numerator of a certain fraction1 it is made equal to one-fifth1 whilst if #b be taken from the denominator it becomes equal to one-sixth4 ,find the fraction4 ,,euclid4--,,the ,,famous ,,forty-,,seventh4 8,in any right-angled triangle1 the square which is described upon the side opposite to the right-angle is equal to the squares described upon the sides which contain the right-angle40 ,here is a simple way of proving this proposition4 ,although perhaps not exactly scholastic1 it is none the less interesting4 ,draw an exact square1 whose sides measure #g in42 then divide it into #di square inches4 ,having done this1 cut the figure in following the big lines as shown by ,fig #a4 ,it will be observed that ,c is a complete square1 and that ,a and ,b will form a square3 but as ,d is #a in4 short of being a square1 it is necessary to cut a square inch and add it on4 ,illustration3 ,fig4 #a4 ,illustration3 ,fig4 #b4 ,then construct a right-angled triangle as shown by ,figure #b4 ,we then see that the sum of the two small squares is equivalent to the large square4 ,d contains #i small squares4 ,a ,b do4 #af do4 -- #be ,and as we see that ,c has #be small squares1 it is thus proved that the sum of the squares upon the sides which contain the right angle are equal to the squares upon the side opposite the right angle4 ,q4,e4,d4 ,,the ,,great ,,fish ,,problem4 #bji4 ,there is a fish the head of which is #i in4 long1 the tail is as long as the head and half the back1 and the back is as long as the head and tail together4 ,what is the length of the fish8 #baj4 ,how may #ajj be expressed with four nines8 #baa4 ,two shepherds1 ,a and ,b1 meeting on the road1 began talking of the number of sheep each had1 when ,a said to ,b1 8,give me one of your sheep1 and ,i will have as many as you40 8,oh1 no60 replied ,b2 8give me one of yours1 and ,i will have as many again as you40 ,how many sheep had each8 ,a ,,brick ,,puzzle4 ,,one ,,for ,,builders1 ,,contractors1 ,c4 #bab4 ,suppose the measurements of a brick to be3--,length1 #i in42 breadth1 #d in42 depth1 #c in4 ,how many 8stretchers1 headers and closures0 can be cut out of one1 and what would be the face area of same8 ,for the benefit of the uninitiated we might say that 8stretcher0 length of brick x depth 8header0 breadth 8closure0 half-breadth #bac4 ,a woman has a basket of #aej eggs2 for every #a goose egg she has #b duck eggs and #c hen eggs4 ,how many of each had she8 ,the ,great ,chess ,problem4 ,,the ,,knight ,,move4 #bad4 ,move the ,knight over all the #fd squares of the chess board so as to successively cover each square and1 of course1 not enter any square twice4 ,this problem has always proved to be an interesting one4 ,mathematicians throughout all ages have devoted a good deal of time to it4 ,to chess players it should be especially attractive4 ,illustration #bae4 ,if #c times a certain number be taken from #g times the same number the remainder will be #h4 ,what is the number8 #baf4 ,divide #bg among #c persons1 ,a1 ,b and ,c1 so that ,b may have twice as much as ,a1 and ,c #c times as much as ,b4 ,,answer ,,this4 #bag4 ,suppose it were possible for a man in ,sydney to start on ,sunday noon1 ,january #ast1 and travel westward with the sun1 so that it might be in his meridian all the time1 he would arrive at ,sydney next day at noon1 ,monday1 ,jan4 #bnd4 ,now1 it was ,sunday noon when he started1 it was noon with him all the way round1 and is ,monday noon when he returns4 ,the question is1 at what point did it change from ,sunday to ,monday8 #bah4 ,start with #a and keep on doubling for eight times1 thus giving nine numbers1 and arrange them in a square that when multiplied together1 horizontally1 vertically1 or diagonally1 the product of each row will be the cube of the number which must go in the centre of the square4 ,the happiest year in a man's life is #dj2 for then he can ,,xl4 ,bound to ,win6 #bai4 ,a certain gentleman1 who was employed in one of our city offices1 purchased ,,the ,,doctrine ,,of ,,chance1 which he studied in his spare time1 with the result that he sent in his resignation to the head of the firm in order to try his luck on the racecourse4 ,at the first meeting he attended1 there were only three horses in a race4 ,his brother bookmakers were crying out the odds-- 8,two to #a bar one40 ,the odds on this latter horse which was 8barred0 he discovered to be #f to #d on4 ,he determined to give far more liberal odds1 and called out-- 8,even money1 #b to #a1 and #c to #a40 ,how could he give such odds1 and yet win #a1 no matter which horse wins the race8 ,illustration ,,an ,,inch ,,of ,,rain4 ,how many people really consider what is contained in the expression8 ,calculated1 it amounts to this3--,an acre is equal to #f1bgb1fdj square inches2 an inch deep of water on this area will be as many cubic inches of water1 which1 at #bggbgd inches to the gallon1 is #bbfbbe gallons4 ,the quantity weighs #bbf1bbe lbs4 ,thus1 an 8inch of rain0 is over #ajj tons of water to the acre4 ,extract from a small boy's first essay3--8,man has two hans4 ,one is the rite han an one is the left han4 ,the rite han is fur ritin1 and the left han is fur leftin4 ,both hans at once is fur stummik ake40 #bbj4 ,find the side of a square whose area is equal to twice the sum of its sides8 8,,the ,,evidence ,,you ,,now ,,give1 c41 c40 #bba4 ,smith1 ,brown1 and ,jones were witnesses in a law case4 ,the first-named gentleman swore that a certain thing occurred2 ,brown1 on being called1 confirmed ,smith's statement1 but ,jones denied it4 ,they are known to tell the truth as follows3-- ,smith1 once in #c times ,brown1 #e ,jones1 #aj ,what is the probability that the statement is true8 ,when a man attains the age of #ij years1 he may be termed ,,xc-dingly old4 ,examination ,gems4 ,a school examination room might not to a casual observer seem to be a very likely place to find entertainment4 ,however1 the answers often given by pupils are sometimes excruciatingly funny1 as is proved by the following3-- ,,definitions4 ,function4--8,when a fellow feels in a funk40 ,quotation4--8,the answer to a division sum40 ,civil ,war4--8,when each side gives way a little40 ,the ,four ,seasons4--8,pepper1 mustard1 salt and vinegar40 ,alias4--8,means otherwise--he was tall1 but she was alias40 ,compurgation4--8,when he was going to have anything done to him1 and if he could get anyone to say1 #8not innocent1' he was let off40 ,the ,equator4--8,means the sun4 ,suppose we draw a straight line and the sun goes up to the top1 then it is day1 and when it comes down it is night40 ,precession4--87#a7 ,when things happen before they take place4 7#b7 ,the arrival of the equator in the plane of the ecliptic before it is due40 ,demagogue4--8,a vessel that holds beer1 wine1 gin1 whisky1 or any other intoxicating liquor40 ,chimera4--8,a thing used to take likenesses with40 ,watershed4--8,a place in which boats are stored in winter40 ,gender4--8,is the way whereby we tell what sex a man is40 ,cynical4--8,a cynical lump of sugar is one pointed at the top40 ,immaculate4--8,state of those who have passed the entrance examination at the ,university40 ,frantic4--8,means wild4 ,i picked up some frantic flowers40 ,nutritious4--8,something to eat that aint got no taste to it40 ,repugnant4--8,one who repugs40 ,memory4--8,the thing you forget with40 ,,history4 8,without the uses of ,history everything goes to the bottom4 ,it is a most interesting study when you know something about it40 8,oliver ,cromwell was a man who was put into prison for his interference in ,ireland4 ,when he was in prison he wrote #8,the ,pilgrim's ,progress1' and married a lady called ,mrs4 ,o',shea40 8,wolsey was a famous ,general who fought in the ,crimean war1 and who1 after being decapitated several times1 said to ,cromwell1 #8,ah1 if ,i had only served you as you have served me1 ,i would not have been deserted in my old age4' ,he was the founder of the ,wesleyan ,chapel1 and was afterwards called ,lord ,wellington4 ,a monument was erected to him in ,hyde ,park1 but it has been taken down lately40 8,perkin ,warbeck raised a rebellion in the reign of ,henry ,,viii4 ,he said he was the son of a ,prince1 but he was really the son of respectable people40 ,which do you consider the greater ,general1 ,csar or ,hannibal8 8,if we consider who ,csar and ,hannibal were1 the age in which they lived1 and the kind of men they commanded1 and then ask ourselves which was the greater1 we shall be obliged to reply in the affirmative40 ,why was it that his great discovery was not properly appreciated until after ,columbus was dead8 8,because he did not advertise40 ,what were the slaves and servants of the ,king called in ,england8 8,serfs1 vassals1 and vaselines40 ,,divinity4 ,parable4--8,a heavenly story with no earthly meaning40 8,esau was a man who wrote fables1 and who sold the copyright to a publisher for a bottle of potash40 ,what is ,divine right8 8,the liberty to do what you like in church40 ,what is a ,papal bull8 8,a sort of cow1 only larger1 and does not give milk40 8,titus was a ,roman ,emperor1 supposed to have written the ,epistle to the ,hebrews4 ,his other name was ,oates40 ,explain the difference between the religious belief of the ,jews and ,samaritans8 8,the ,jews believed in the synagogue1 and had their ,sunday on a ,saturday2 but the ,samaritans believed in the ,church of ,england and worshipped in groves of oak2 therefore the ,jews had no dealings with the ,samaritans40 ,give two instances in the ,bible where an animal spoke8 87#a7 ,balaam's ass4 7#b7 ,when the whale said unto ,jonah1 #8,almost thou persuadest me to be a ,christian4'0 ,,mathematics4 ,a ,problem4--8,something you can't find out40 ,hypotenuse4--8,a certain thing is given to you1 or it means let it be granted that such and such a thing is equal or unequal to something else40 8,if there are no units in a number you have to fill it up with all zeros40 8,units of any order are expressed by writing in the place of the order40 8,a factor is sometimes a faction40 8,if fractions have a common denominator1 find the difference in the denominator40 8,interest on interest is confound interest40 ,,grammar4 8,grammar is the way you speak in #i different parts of speech2 it is an art divided in #d quarters--tortology is one1 and sintax one more40 ,an ,abstract ,noun4--8,something you can think of1 but not touch--a red-hot poker40 ,an ,article4--8,that wich begins words and sentences40 ,a ,pronoun 8is when you don't want to say a noun1 and so you say a pronoun40 8,a ,adjective is the colour of a noun1 a black dog is a adjective40 8,adjectives of more than one syllable are repaired by adding some more syllables40 8,nouns are the names of everything that is common and has a proper name40 ,verb4--8,to go for a swim is a verb what you do40 8,adverbs are verbs that end with a lie and distinguish words4 ,it is used to mortify a noun1 and is a person1 place1 or thing1 sometimes it is turned into a noun and then becomes a noun or pronoun40 8,preposition means when you say anything of anything40 8,conjunction means what joins things together2 #8--and #b men shook hands4'0 8,nouns denoting male and female and things without sex is neuter4 #8,the cow jumped over the fence' is a transitif nuter verb because fence isen't the name of anything and has no sex40 ,interjection4--8,words which you use when you sing out40 8,gender is how you tell what sex a man is40 ,which ,hand is ,it ,in8 ,illustration ,a person having in one hand a piece of gold1 and in the other a piece of silver1 you may tell in which hand he has the gold1 and in which the silver1 by the following method3-- ,some even number 7such as #h7 must be given to the gold1 and an odd number 7such as #c7 must be given to the silver2 after which1 tell the person to multiply the number in the right hand by any even number whatever1 and that in the left hand by an odd number2 then bid him add together the two products1 and if the whole sum be odd1 the gold will be in the right hand and the silver in the left2 if the sum be even1 the contrary will be the case4 ,to conceal the artifice better1 it will be sufficient to ask whether the sum of the two products can be halved without a remainder--for in that case the total will be even1 and in the contrary case odd4 #bbb4 ,which is the heavier1 and by how much--a pound of gold or a pound of feathers2 an ounce of gold or an ounce of feathers8 #bbc4 ,plant an orchard of #ba trees1 so that there shall be #i straight rows with #e trees in each row1 the outline to be a regular geometrical figure4 ,,settling ,,up4 #bbd4 ,a person paid a debt of #e with sovereigns and half-crowns4 ,now1 there were half the number of sovereigns that there were half-crowns4 ,how many were there of each8 ,a 8,,catch40 #bbe4 ,how can you rub out #bj marks on a slate1 have only five rubs1 and rub out every time an odd one8 #bbf4 ,from six take nine1 from nine take ten1 ,from forty take fifty1 and six will remain4 #bbg4 ,a man and his wife lived in wedlock1 one-third of his age and one-fourth of hers4 ,now1 the man was eight years older than his wife at marriage1 and she survived him #bj years4 ,how old were they when married8 ,,to ,,prove ,,that ,,you ,,have ,,eleven ,,fingers4 ,count all the fingers of the two hands1 then commence to count backwards on one hand1 saying1 8#aj1 #i1 #h1 #g1 #f0 7with emphasis on the #f71 and hold up the other hand saying1 8and #e makes #aa40 ,this simple deception has often puzzled many4 #bbh4 ,a man travelled a certain journey at the rate of four miles an hour1 and returned at the rate of three miles an hour4 ,he took #ba hours in going and returning4 ,what was the total distance gone over8 #bbi4 ,from what height above the earth will a person see one-third of its surface8 #bcj4 ,the difference between #ag_/ba and #aa_/ad of a certain sum is #aj4 ,what is the sum8 #bca4 ,what decimal fraction is a second of a day8 #bcb4 ,two trains are running on parallel lines in the same direction at rates respectively #de miles and #ce miles an hour2 the length of the first is #ag yds4 #b ft41 and of the second #gj yds4 #a ft4 ,how long will the one be in passing the other8 #bcc4 ,suppose a bushel to be exactly round1 ,and the depth1 when measured1 eight inches be found2 ,if the breadth #ahghi inches you discover1 ,this bushel is legal all ,england over3 ,but a workman would make one of another frame1 ,seven inches and a half the depth of the same2 ,now say of what length must the diameter be1 ,that it may with the former in measure agree4 ,,worth ,,trying4 ,a well known writer on mathematics1 and a member of the ,academy of ,science1 ,paris1 says that the most skilful calculator could not in less than a month find within a unit the cube root of #fifecfdhccahfdjjcejgcfdajcg4 ,a ,,problem ,,that ,,worried ,,the ,,ancients4 ,many profound works have been written on the following famous problem3-- 8,when a man says #8,i lie1' does he lie1 or does he not8 ,if he lies he speaks the truth2 if he speaks the truth he lies40 ,several philosophers studied themselves to death in vain attempts to solve it4 ,reader1 have a 8go0 at it4 ,,the ,,cabinet ,,maker',s ,,puzzle4 #bcd4 ,a cabinet maker has a circular piece of veneering with which he has to veneer the tops of two oval stools2 but it so happens that the area of the stools1 exclusive of the hand-holes in the centre and that of the circular piece1 are the same4 ,how must he cut his veneer so as to be exactly sufficient for his purpose8 ,,the ,,arithmetical ,,triangle4 #a #b1 #a #c1 #c1 #a #d1 #f1 #d1 #a #e1 #aj1 #aj1 #e1 #a #f1 #ae1 #bj1 #ae1 #f1 #a #g1 #ba1 #ce1 #ce1 #ba1 #g1 #a #h1 #bh1 #ef1 #gj1 #ef1 #bh1 #h1 #a ,write down the numbers #a1 #b1 #c1 c41 as far as you please in a column4 ,on the right hand of #b place #a1 add them together and place #c under the #a2 the #c added to #c #f1 which place under the #c1 and so on2 this gives the second column4 ,the third is found from the second in a similar way4 ,by the triangle we can determine how many combinations can be made1 taking any number at a time out of a larger number4 ,for instance1 a group of #h gentlemen agreed that they should visit the ,crystal ,palace #c at a time1 and that the visits should be continued daily as long as a different three could be selected4 ,in how many days were the possible combinations of #c out of #h completed8 ,,method3 ,look down the first column till you come to #h1 then see what number is horizontal with it in the third column1 viz41 #ef4 7,for the method usually adopted for working out calculations like the above1 see ,,doctrine ,,of ,,chance47 #bce4 ,why is a pound note more valuable than a sovereign8 ,,keeping ,,up ,,style4 #bcf4 ,a certain hotelkeeper was never at a loss to produce a large appearance with small means4 ,in the dining-room were three tables1 between which he could divide #ba bottles of wine1 of which #g only were full1 #g half-full1 and #g apparently just emptied1 and in such a manner that each table had the same number of bottles and the same quantity of wine4 ,how did he manage it8 ,a ,,domino ,,trick4 ,ask the company to arrange the whole set of dominoes whilst you are absent in any way they please1 subject1 however1 to domino rules--a #f placed next to a #f1 a #e to a #e1 and so on4 ,you now return and state that you can tell1 without seeing them1 what the numbers are at either end of the chain4 ,the secret lies in the fact that the complete set of #bh dominoes1 arranged as above-mentioned1 forms a circle or endless chain4 ,if arranged in a line the two end numbers will be found to be the same1 and may be brought together1 completing the circle4 ,you privately abstract one domino 7not a double71 thus causing a break in the chain4 ,the numbers left at the ends of the line will then be the same as those of the 8missing link0 7say the #c-e or #f-b47 ,the trick may be repeated1 but you must not forget to exchange the stolen domino for another4 #bcg4 ,a busman not having room in his stables for eight of his horses increased his stable by one half1 and then had room for eight more than his whole number4 ,how many horses had he8 ,,an ,,ancient ,,question4 #bch4 8,tell us1 illustrious ,pythagoras how many pupils frequent thy school80 8,one-half10 replied the philosopher1 8study mathematics1 one fourth natural philosophy1 one-seventh observe silence1 and there are #c females besides40 ,how many had he8 ,,evading ,,the ,,question4 #bci4 ,a lady being asked her age1 and not wishing to give a direct answer1 said1 8,i have nine children1 and three years elapsed between the birth of each of them4 ,the eldest was born when ,i was #ai years old1 and the youngest now is exactly #ai40 ,how old was she8 ,a ',,centage 8,,catch40 #bdj4 ,a man sells a diamond for #fj2 the number expressing the profit per cent4 is equal to half the number expressing the cost4 ,what was the cost8 #bda4 ,having #e hours to spare1 how far may ,i go out by a coach at the rate of #h miles an hour so that ,i may be back in time1 walking at the rate of three miles an hour8 ,the ,cross ,puzzle4 ,illustration #bdb4 ,cut out of a piece of card five pieces similar in shape and proportion to the annexed figures4 #a piece similar to #a #c pieces #b #a piece #c ,these five pieces are then to be so joined as to form a cross like that represented by #d4 ,irish ,counting4 ,an ,irishman who had lately arrived in the colony was employed as handy man at one of our large suburban mansions4 ,the lady of the house1 hearing that some midnight thief had walked off with some of her prize poultry1 desired ,pat to count them as speedily as possible and to inform her how many there were2 he accordingly left off cleaning the buggy1 and proceeded to enumerate the feathered bipeds4 ,the lady1 getting impatient of waiting for him1 repaired to the poultry yard1 and noticing him chasing a small chicken1 enquired1 8,pat1 whatever are you doing60 when the ,irishman replied2 8,i've counted all the chickens except this one2 but the little varmint won't stand still till ,i count him40 ,,the ,,jew 8,,jewed40 #bdc4 ,an old ,jew took a diamond cross to a jeweller to have the diamonds re-set1 and fearing that the jeweller might be dishonest he counted the diamonds1 and found that they numbered #g in three different ways4 ,now1 the jeweller stole two diamonds1 but arranged the remainder so that they counted #g each way as before4 ,how was it done8 #g #f #g #f #e #f #g #d #c #b #a #bdd4 ,a person wishing to enclose a piece of ground with palisades found that if he set them a foot apart that he should have too few by #aej1 but if he set them a yard apart he should have too many by #gj4 ,how many had he8 #bde4 ,a mechanic is hired for #fj days on consideration that for each day he works he shall receive #gs4 #f;d41 but for each day he is idle he shall pay #bs4 #f;d4 for his board1 and at the end he receives #f4 ,how many days did he work8 #bdf4 ,take one from nineteen and leave twenty4 ,,the ,,camel ,,problem4 ,illustration #bdg4 ,an ,arab ,sheik1 when departing this life1 left the whole of his property to his three sons4 ,the property consisted of #ag camels1 and in dividing it the following proportions were to be observed3-- ,the oldest son was to have one-half of the camels1 the second son one-third1 and the youngest son one-ninth2 but it was provided that the camels were not1 on any account1 to be injured1 but to be divided as they were--living--between the three sons4 ,thereupon1 a great argument ensued4 ,the eldest son claimed #h camels4 ,the second insisted upon receiving #e of a camel2 while the youngest son would not be comforted with less than #a-h_/i of a camel4 ,the ,cadi 7or ,judge7 happened to appear on the scene4 ,to him the matter was explained4 ,without a moment's hesitation he gave his decision--a decision by which the claims of all three contestants were fully satisfied4 ,how did the ,cadi settle this knotty question8 #bdh4 ,a grocer has #f weights--each one twice as much as the one before it in size4 ,if he weighed the first five against the largest1 it 7the largest7 would only be #b lbs4 heavier than the combined weights of the rest4 ,what are the weights8 #bdi4 ,a squatter said to a new manager1 whom he wished to test in arithmetic3 8,i have as many pigs as ,i have cattle and horses1 and if ,i had twice as many horses ,i should then have as many horses as cattle1 and ,i should also have #ac more cattle and horses than pigs40 ,how many of each had he8 #bej4 ,a gentleman a garden had1 five score#b long and four score broad2 ,a walk of equal width half round he made1 which took up half the ground-- ,you skilful in ,geometry1 tell us how wide the walk must be4 #b ,feet4 #bea4 ,two boys1 meeting at a farmhouse1 had a mug of milk set down to them2 the one1 being very thirsty1 drank till he could see the centre of the bottom of the mug2 the other drank the rest4 ,now1 if we suppose that the milk cost #d;d41 and that the mug measured #d inches diameter at the top and bottom1 and #f inches in depth1 what would each boy have to pay in proportion to the milk he drank8 ,weight-for-,age ,problem4 #beb4 ,there are #f children seated at a table whose total ages amount to #ci years4 ,tom1 who is only half the age of ,jack 7the oldest7 is seated at the top1 with ,bob--who is a year older than him--next2 whilst ,fred1 who is four-fifths the age of ,jack1 is at the foot with ,james1 who is #a year younger than ,jack1 next1 him2 the youngest1 who is a baby1 is one-eighth the age of her brother ,fred4 ,find the ages of each1 and weight of ,fred1 and by placing him third from the top his initial and surname4 ,you must express the ages in words1 and use the initial letters4 #bec4 ,a flagstaff there was whose height ,i would know1 ,the sun shining clear straight to work ,i did go4 ,the length of the shadow1 upon level ground1 ,just sixty-five feet1 when measured ,i found2 ,a pole ,i had there just five feet in length-- ,the length of its shadow was four feet one-tenth ,how high was the flagstaff ,i gladly would know2 ,and it is the thing you're desired to show4 #bed4 ,put #d figures together to equal #cj1 and the same figures to equal #dj4 #bee4 ,a ,salvation ,army captain took up a collection1 his lieutenant took up another2 if what the captain took up was squared and the lieutenant's added the sum would be #aa;d42 if what the lieutenant took up was squared and the captain's added the sum would be #g;d4 ,what was the amount of the collection8 #bef4 ,find a number which1 if multiplied by #ag1 gives a product consisting only of #c's4 ,,the 8,,fowl0 ,,problem4 #beg4 ,if a hen and a half lay an egg and a half in a day and a half1 how many eggs will #f hens lay in #g days8 #beh4 ,tom and ,bill work #e days each4 ,tom has as much and half as much per day as ,bill4 ,the total amount of their wages for the #e days is #a #ags4 #f;d4 ,what are their respective wages per day8 #bei4 ,how many inch cubes can be cut out of a #b inch cube8 #bfj4 miles4 furl4 po4 yds4 ft4 in4 ,from #a #j #j #j #j #j ,subtract #g #ci #e #a #e ------------------------------ ,,the ,,square ,,puzzle4 ,illustration #bfa4 ,a man has a square of land1 out of which he reserves one-fourth 7as shown in the diagram7 for himself4 ,the remainder he wishes to divide among his four sons so that each will have an equal share and in similar shape with his brother4 ,how can he divide it8 ,although this is a very old puzzle it is often the cause of much amusement4 ,,generous4 #bfb4 ,a gentleman1 having a certain number of shillings in his possession1 made up his mind to visit #ag different barracks and treat the soldiers1 and he did so in the following manner3--,on going into the first barracks1 he gave the sentry one shilling and then spent half of his shillings in the canteen amongst the soldiers1 and on coming out of barracks again he gave the sentry another shilling2 he repeated the same until he had finished with the seventeenth barracks1 and had no more shillings left4 ,how many had he when he commenced8 #bfc4 ,what part of #c is a third part of #b8 #bfd4 ,make #ia less by adding two figures to it4 #bfe4 ,if a church bell takes two seconds to strike the hour at #b o'clock1 how many seconds will it take to strike #c o'clock8 ,,this ,,catches ,,everybody4 ,ask a friend how many penny stamps make a dozen8 ,he will reply1 8,why1 twelve1 of course40 ,then ask again1 8,well1 how many half-penny ones80 ,he is almost sure to reply1 8,twenty-four40 ,before he settles his account with nature1 man charges the debit of his profit and loss account to ,fate1 but the credit he takes to himself4 ,,the ,,puzzle ,,about ,,the 8,,profits40 ,perhaps there is no form of commercial calculation so confusing and so little understood as that of mercantile profits4 ,it might surprise many to state1 nevertheless it is perfectly true1 that it is impossible to buy goods and sell them to show a profit as great as #ajj per cent4 ,the correct method to calculate profit is to reckon on the return--the price received for the goods sold--not on the cost price1 and as it is impossible to sell goods at #ajj per cent4 discount1 so also goods cannot be sold to show that percentage of profit1 unless they actually cost nothing4 ,some time ago1 in ,new ,zealand1 a well-known boot manufacturer had a 8,,great ,,discount ,,sale48 ,he had large posters displayed on the windows of his shops1 and advertisements in the newspapers1 announcing the fact that #es4 in the would be allowed as discount to all customers4 ,the profit he usually obtained in the ordinary way of trade was #be per cent41 and having had a good season1 he was prepared to sell off the balance of his stock at cost price4 ,the selling price of his goods was marked in plain figures4 ,a pair of boots which cost him #hs4 was marked #ajs41 thus showing a profit of #bs41 which he considered to be #be per cent4 7#bs4 being a quarter of #hs47 ,instructions were issued to all his employees engaged in selling to deduct a quarter from the marked price1 the result being that a pair of boots which cost #hs41 and marked #ajs41 was being sold at #gs4 #f;d4 7#bs4 #f;d41 the quarter of the marked price being deducted from #ajs47 ,although he imagined he was getting #be per cent4 profit1 he was in reality receiving only #bj per cent4 ,it was not long before the posters were altered1 announcing that #ds4 in the would be allowed to his customers4 ,the following question was asked some little time ago2--,if a chemist sold a bottle of medicine for #bs4 #f;d41 which cost him #b;d41 what percentage would be his profit8 ,many work out the problem and answer #aajj per cent41 but this answer is incorrect4 ,he received #bs4 #f;d4 for that which cost him #b;d41 accordingly there was a profit of #bs4 #c;d4 ,we must now find out what percentage is the latter amount of the selling price1 #bs4 #f;d41 and we discover that it is #ia per cent4 #bff4 ,a pork butcher buys at auction #ajj worth of bacon at #d;d4 per lb4 and sells it at #h;d4 per lb42 also #ajj worth at #h;d4 per lb41 which he sells for #d;d4 per lb4 ,does he lose or gain8 ,and if so how much4 8,,the ,,jumping ,,frog40 #bfg4 ,a frog1 sitting on one end of a log eight feet long1 starts to jump into a pond at the opposite end4 ,with his first jump he clears half the distance1 the second jump half the remaining distance1 and so on4 ,how many jumps does he take before entering the pond8 ,,oblong ,,puzzle4 #bfh4 ,cut out of a piece of cardboard fourteen pieces of the same shape as those shown in the diagram--the same number of pieces as is there represented--and then form an oblong with them4 ,illustration #bfi4 ,if a man can load a cart in five minutes1 and a friend can load it in two and a half minutes1 how long will it take them both to load it1 both working together8 #bgj4 ,a gentleman on being asked how old he was1 said that if he did not count ,mondays and ,thursdays he would be #ce4 ,what was his actual age8 ,,too ,,smart ,,for ,,dad4 8,pa10 said a boy from school1 8,how many peas are in a pint80 8,how can anybody tell that1 foolish boy80 8,i can every time4 ,there is just one #8p' in pint the world over40 ,he was sent off to bed early4 ,,simple ,,proportion4 #bga4 ,if it takes three minutes to boil one egg1 how long will it take to boil two8 8,,punch',s0 ,,money ,,vagaries4 ,the early ,italians used cattle as a currency instead of coin 7thus a bull equals #es47 and a person would send for change for a thousand pound bullock1 when he would receive #bjj five pound sheep4 ,if he wanted very small change there would be a few lambs amongst them4 ,the inconvenience of keeping a flock of sheep at one#8s bankers'1 or paying in a short-horned heifer to one's private account led to the introduction of bullion4 ,as to the unhealthy custom of sweating sovereigns1 it may be well to recollect that ,charles ,i41 the earliest ,sovereign1 who was sweated to such an extent that his immediate successor1 ,charles ,,ii41 became one of the lightest ,sovereigns ever known in ,england4 ,formerly every gold watch weighed so many carats1 from which it became usual to call a silver watch a turnip4 ,the ,romans were in the habit of tossing their coins in the presence of their legions1 and if a piece of money went higher than the top of their ,ensign's flag it was presumed to be 8above the standard40 8,,march ,,on6 ,,march ,,on60 #bgb4 ,an army #be miles long starts on a journey of #ej miles1 just as an orderly at the rear starts to deliver a message to the ,general in front4 ,the orderly1 travelling at a uniform speed1 delivers his message and returns to the rear1 arriving just as the army finishes the journey4 ,how many miles does the orderly travel8 8,,with ,a ,,long1 ,,long ,,pull40 ,illustration #bgc4 ,if eight men are engaged in a tug-o'-war1 four pulling against four1 on a continuous rope1 and each man is exerting a force of #ajj lbs41 what strain is there at the centre of the rope8 8,,find ,,out40 #bgd4 ,a gentleman in a train with a boy got into conversation with a stranger1 who asked him the lad's age4 ,the boy quickly replied1 8,this gentleman1 who is my uncle1 is twice as old as me1 but the sum of the figures in my age are twice the sum of those in his40 ,what was the age of each8 #bge4 ,one of our squatters who had made his fortune in the 8good times0 determined to sell his run and spend the rest of his days in the old country4 ,a new chum1 possessing considerable wealth1 and desirous of settling down in ,australia1 hearing of the squatter's intention1 interviewed him with the object of purchasing1 when the following conversation ensued3-- ,,new ,,chum3 8,how big is your run8 ,what's its area80 ,,squatter3 8,well1 ,i'm blessed if ,i know1 but ,i can tell you it's perfectly square and enclosed with posts and rails4 ,each of the rails is #i ft4 long40 ,,new ,,chum3 8,oh1 then1 is it what you call a three-railed paddock80 ,,squatter3 8,yes1 that's so1 and now ,i remember that the number of rails in my run is equal to the number of acres4 ,if you like you can take a horse and ride round and count the rails1 then you will know the area40 ,this advice the new chum acted upon4 ,find out the length of his ride and the area of the run4 ,a ,federal ,problem4 ,it is well known to our readers that paper money--such as pound notes--issued in one colony are depreciated in another2 thus a one pound note of ,n4,s4,w4 is only worth #ais4 #f;d4 in ,victoria1 and vice versa4 ,some time ago a rather 'cute individual in ,wodonga1 on the ,victorian side of the border1 bought a drink in a local hotel with a ,victorian note1 and received in change a ,n4,s4,w4 note1 which was worth then and there only #ais4 #f;d42 he thereupon crossed the ,murray to ,albury on the ,new ,south ,wales side1 bought another drink for sixpence with his ,n4,s4,w4 note1 and received a ,victorian note equal to #ais4 #f;d4 in change4 ,he travelled backwards and forwards during the day1 getting his twentieth and last drink in ,albury1 on the ,n4,s4,w4 side1 whereupon he returns to ,wodonga with a ,victorian pound note still to his credit4 ,he thus paid for all his drinks1 which amounted to ten shillings4 ,who lost the money8 ,we cannot advise readers to 8go thou and do likewise10 for the simple reason that such a proceeding would now be impossible1 as exchange is no longer charged in the two towns mentioned4 ,it is not until we get further from the border that the levy is made4 ,doing ,two ,things at ,once4 ,an inspector was examining a school in a country district some distance from a railway station4 ,he was afraid of losing his train1 so hurrying with his work he tried to do two things at once4 ,standing in the doorway1 he gave out dictation to ,class ,,iii4 in the main room1 and at the same time gave out a sum to ,class ,,iv4 in an adjoining room1 jerking out a few words alternately4 ,the sum was 8,if a couple of fat ducks cost #ais41 how many can he get for #gb #ajs4 #i;d40 ,the dictation for ,class ,,iii4 began 8,now as a lion prowling about in search1 c40 ,of course the poor children heard both1 and got a bit mixed4 ,one little girl's dictation began 8,now a couple of ducks prowling about in search of a lion who had lost #ais41 c40 ,while a ,class ,,iv4 lad was scratching his head over the following sum 8,if #gb couples of fat lions cost #ais41 how much prowling could be got for #gb #ajs4 #i;d40 ,,two ,,calendar ,,catches4 ,ask a person if ,christmas ,day and ,new ,year's ,day come in the same year4 ,the answer generally given is 8,of course not1 ,christmas comes in this year1 and ,new ,year's ,day in the next40 ,another question that often puzzles many4 ,have we had more ,christmas days than ,good ,fridays8 ,the usual answer is 8,no1 both the same40 #bgf4 ,a brass memorial tablet in honour of the late ,sir ,charles ,lilley has been fixed in the centre of the eastern wall of the ,brisbane ,grammar ,school ,hall4 ,the enthusiasm displayed by ,sir ,charles in the cause of education generally1 and his work on behalf of the ,grammar ,school1 make this commemoration particularly appropriate4 ,the following is the inscription1 to translate which should prove a capital exercise to all ,latin scholars4 ,the tablet measures #ej inches by #cj inches4 ,illustration3 ,,memorial ,,tablet ,,to ,,the ,,late ,,sir ,,charles ,,lilley ,it may be added that the lettering of the plate was designed by ,mr4 ,r4 ,s4 ,dods1 architect1 and the engraving was done in ,brisbane by ,messrs4 ,randle ,bros41 the well-known engravers1 of ,elizabeth ,street4 ,a ,puzzle in ,book-keeping4 #bgg4 ,a firm appointed an agent to do business on their account1 and gave him #cb #ags4 in cash for expenses1 c41 and also supplied him with a stock of goods1 the value wholesale being #eg #ads42 while in a distant town he bought a job lot of goods for #ei #ais41 which he paid cash for out of what he had realised on his first stock4 ,he still continued to sell1 but very soon after the firm called him in1 and desired him to close his account and hand in a full statement4 ,his total retail sales amounted to #ajb #ags41 and he returned goods to the value of #ca #ags41 his expenses had been #be4 ,question--,what does the firm owe the agent1 or the agent owe the firm8 ,,the ,,agent',s ,,statement ,,being-- ,cash #cb #ag ,goods #eg #ad ,paid for ,goods #ei #ai ,cash ,sales #ajb #ag ,goods ,returned #ca #ag ,expenses #be #j ,this puzzle first appeared in 8,,how ,,to ,,become ,,quick ,,at ,,figures10 the answer being withheld4 ,it is a record of transactions that actually occurred in ,america1 which were the subject of litigation4 ,although we received thousands of replies1 not more than #e per cent4 were correct4 ,it is a question that individuals not conversant with book-keeping would be as likely to solve correctly as the expert4 ,for the convenience of those who are unacquainted with ,american money we have been obliged to substitute s4 d41 and would advise our readers to attempt a solution before referring to the answer4 ,,conclusion4 ,in bringing 8,,the ,,puzzle ,,king0 to a conclusion1 the author can only express the hope that he has been successful in his endeavour to make it not only an amusing work but also a useful one4 ,the impossibility of making a book of this nature perfect is fully recognised1 and corrections or contributions will be cordially received1 and the contributor liberally remunerated4 ,all communications must be sent to #dd ,pitt ,street1 ,sydney1 addressed to the author1 who tenders to all readers of 8,,the ,,puzzle ,,king0-- ,,an ,,arithmetical ,,toast4 8,here's an addition to your wages4 ,here's a subtraction from your wants and miseries4 ,here's a multiplication of your joys and happiness4 ,here's a division amongst your enemies4 ,here's a reduction of your hours of labour4 ,and here's a hope that you'll all be able to practice and take interest in 8,,the ,,puzzle ,,king40 ,answers4 7#a7 #ab1aaa4 7#b7 #bds4 7#c7 #ah4 7#d7 ,he lost #ac #fs4 #h;d4 7#e7 -------------------- #dhe #dfc #dge #dfe -------------------- #dfa #dfg #dhg #dgc -------------------- #dhc #dgg #deg #dga -------------------- #dei #dha #dfi #dgi -------------------- 7#f7 ,see ,no4 #bbe4 7#g7 #cj4 7#h7 #fge springs4 7#i7 ,illustration 7#aj7 ,suppose a man and woman to marry1 the man to have had a son by a former marriage 7the gentleman who leaves the money72 also the woman has a daughter by a former marriage4 ,this son and daughter get married1 and have a son4 ,this is the scheme of kindred1 and answers the conditions of the paradox4 7#aa7 #d;d4 ,there were three of them--grandfather1 father1 and son4 7#ab7 ,the total score was #bdj4 ,the #ast player scored #cj2 the #bnd and #crd1 #bd each2 the #dth1 #eth1 and #fth1 #ab each2 the #gth1 #hth1 #ith1 and #ajth1 #cj each2 and the #aath1 #f4 7#ac7 ,they tip the pail over horizontally2 if any part of the bottom can be seen without spilling the milk it is not half full4 7#ad7 ,in #i-fh_/gh days4 7#ae7 ,the measurements given would not make a triangle4 7#af7 #fdjj soldiers4 7#ag7 ,illustration 7#ah7 ,the ,,left ,,bower4 7#ai7 ,the first #ae second #h third #aj fourth #f --- ,the man had #ci 7#bj7 ,the first boat #ae min4 #de secs41 the second #af min4 7#ba7 #c animals4 7#bb7 ,a comma4 7#bc7 #ae and #aj4 7#bd7 #ba and #ed4 7#be7 #abf4 7#bf7 #gb persons4 7#bg7 #bjghdf inches2 #bjcfdf square inches4 7#bh7 #aa plus #aa #aba #aa x #aa #aba 7#bi7 ,coach fare #cs4 7#cj7 ,the distance from the ends of the least side on the largest and intermediate sides are respectively #baa and #agf links4 7#ca7 #fj4 7#cb7 ,t wins--distance #ij miles2 walking pace--,t #e miles per hour1 ,d #d4 7#cc7 --------------------------- ,a ,b ,c ,d ,e ,f ,g ,h ,i --------------------------- ,my friends1--,i have spare blankets1 and ,i shall need no more2 ,the tenth man can have my bed1 and ,i'll sleep on the floor4 ,in room marked ,a two men were placed2 the third was lodged in ,b2 ,the fourth to ,c was then assigned1 the fifth retired to ,d2 ,in ,e the sixth he tucked away1 in ,f the seventh man1 ,the eighth and ninth in ,g and ,h1 and then to ,a he ran 7,wherein the host1 as ,i have said1 had laid two travellers by72 ,then taking one--the tenth and last--he lodged him safe in ,i3 ,nine spare rooms--a room for each--were made to serve for ten4 ,and this it is that puzzles me and many wiser men4 7#cd7 #gh #gs4 #jdb;d4 7#ce7 #bgefbe leaves4 7#cf7 ,illustration3 ,fig #a 7#cg7 #bdjjj men4 7#ch7 #djcb lines4 7#ci7 #bhi miles4 7#dj7 #bf #gs4 #g;d4 7#da7 #g and #a4 7#db7 ---------------------------- #dg #eh #fi #hj #a #ab #bc #cd #de #eg #fh #gi #i #aa #bb #cc #dd #df #fg #gh #h #aj #ba #cb #dc #ed #ef #gg #g #ah #bj #ca #db #ec #ee #ff #f #ag #ai #cj #da #eb #fc #fe #gf #af #bg #bi #dj #ea #fb #fd #ge #e #bf #bh #ci #ej #fa #gb #gd #d #ae #cf #ch #di #fj #ga #gc #c #ad #be #cg #dh #ei #gj #ha #b #ac #bd #ce ---------------------------- 7#dc7 #h #c #d #a #e #i #f #g #b 7#dd7 ,don't be ,a flat be ,a sharp4 7#de7 #di4 7#df7 ----------- #c #c #c #c #c #c #c #c ----------- ----------- #d #a #d #a #a #d #a #d ----------- 7#dg7 ,give the last person an egg on the dish4 7#dh7 #bj lbs4 7#di7 #a wether1 #aj ewes1 #i lambs4 7#ej7 #ae hours4 7#ea7 #ab square miles4 7#eb7 #g persons4 7#ec7 ,the versed sine of the segment of ,will's cake which was given to ,jack was #cje inches1 and its area #bfjjehcfdcge square inches3 hence ,will's share was #gjdfabeacefbe square inches1 and ,jack's share #gjdeiadcfdcge square inches2 so that ,will's four were about #ebjcbge square inches more than ,jack's six1 and ,will1 of course1 lost the wager4 ,after the decision of the gauger1 ,will's share was #jbajggabde 7#a-ejth nearly7 of a square inch more than ,jack's4 7#ed7 #hdfhea seconds velocity1 #abich ft4 per second4 7#ee7 #add minutes4 7#ef7 #ci #ab ----- #gh #ci ----- #dfh 7#eg7 #hhce yds4 7#eh7 #beacbh sq4 yds nearly4 7#ei7 ,a #ac times1 ,b #h4 7#fj7 ,her son4 7#fa7 #c wickets4 7#fb7 ,not fully stated--suppose #d miles per hour4 7#fc7 #bb plus #b eq4 #bd2 #cc-c eq4 #bd4 7#fd7 #as4 #aa;d4 or #aas4 #a;d4 7#fe7 ,,tobacco4 7#ff7 #a ft4 #efbfh inches4 7#fg7 ,illustration 7#fh7 ,age #bh4 7#fi7 #h_/i 7#gj7 ,illustration3 #a #b #c #d #e #f #g #h #i #aj #d on #a1 #f on #i1 #h on #c1 #e on #b1 and #aj on #g4 7#ga7 ,they put one plank across the angle2 the end of the other resting on it will reach the island4 7#gb7 #bhc2 #bbd4 7#gc7 #bc2 #bd4 7#gd7 ,gallons #abjgde1 diameter #f ft41 height #f ft1 #aj in4 7#ge7 #gf2 #bd4 7#gf7 ,one travels ,west and the other ,east going round the world once a year2 one will gain one day per annum1 and the other will lose a day4 ,in #ej years the difference will amount to #ajj days4 7#gg7 ,diameter #hgjcb miles1 circumference #bgcebi miles1 area #bchjeggeibh miles4 7#gh7 --------------- #fba #fdb #fbg #fcf #fcj #fbd #fcc #fah #fci --------------- 7#gi7 ,the two ends of the box are placed so that they lap over the two sides1 and the wood being one inch thick the length is thus increased by #b inches4 7#hj7 #ifs4 7#ha7 ,first #be #es41 second #bh #es41 third #cj #es41 fourth #cf #es4 7#hb7 ,illustration 7#hc7 7#e-e_/e7e4 7#hd7 #aj inches4 7#he7 #e miles #acjj yds4 7#hf7 #aj4 7#hg7 #aj1 #bb1 #bf4 7#hh7 #ihgfedcba #de #eeeeeeeee #de #abcdefghi #de or #iiiii #de --------- --------- #hfdaigecb #de #eeedeeeef #de 7#hi7 ,the #ast part #h add #b #aj #bnd #ab subtract #b #aj #crd #e multiply by #b #aj #dth #bj divide by #b #aj ---- #de 7#ij7 #cjbe4 #cj plus #be #ee which squared is #cjbe #ihja4 #ih plus #ja #ii which squared is #ihja 7#ia7 #c children4 7#ib7 #cf inches4 7#ic7 ,the difficulty is to determine what would have been the will of the testator had he foreseen that his wife would be delivered of twins4 ,as he desired that in case his wife brought forth a son he should have of his property1 and the mother 1 it follows that his intention was to give his son a sum double to that of the mother2 and as he desired in the other case that if she brought forth a daughter the mother should have and the daughter 1 there is reason to conclude that he intended the share of the mother to be double that of the daughter2 consequently1 to unite these two conditions1 the heritage must be divided in such a manner that the son may have twice as much as the mother1 and the mother twice as much as the daughter4 ,thus we get-- ,son's share1 #djjj ,mother's #bjjj ,daughter's #ajjj ,sometimes the following difficulty is proposed in regard to this problem3--,in case the mother should have two sons and one daughter1 in what manner must the property be divided then8 ,we refer you to the lawyers4 7#id7 #bc years #bhi days--a little less than #bd years4 7#ie7 ,illustration 7#if7 #afej ft4 deep2 #a minutes4 7#ig7 ,illustration 7#ih7 ,man1 #fi yrs #ab weeks ,woman1 #cj yrs #dj weeks 7#ii7 ,a #ah hours1 ,b #bb4 7#ajj7 #c and #b4 7#aja7 #ab pence4 7#ajb7 #ejs4 7#ajc7 ,it is used so in the question4 ,the answer generally given is found in the ,bible 7,judges xvi1 #g and #h74 ,samson was bound with 8seven green withs40 7#ajd7 #cb or #df or #ie-gb_/cf or #ad #eg #ce #a-h_/d #gf --- --------- #hi #ag #ajj #e --- #a #ih #c --- #f #b #ih --- #d #ajj #b --- --- #ajj #ajj 7#aje7 #ef or #bj or #dj #bd #h #cf --- #hj #g #ae #a #ce #g #i #df #ih #c #ai #b --- --- #g #ajj #ajj --- #ajj 7#ajf7 #dd feet4 7#ajg7 #h persons4 7#ajh7 #h4 7#aji7 ,the stone should fall into his hand4 7#aaj7 #f days4 7#aaa7 #e #hs4 #f;d4 7#aab7 ,,ten 7#aac7 ,to explain this often causes much confusion4 ,we must take a simple illustration3 ,i have a garden containing #aj appletrees1 all bearing fruit4 ,now1 there are more trees than any tree has apples on it2 there must be at least #b trees having the same number of apples--for instance1 if ,no4 #a tree has #a apple1 ,no4 #b has #b1 and so on to ,no4 #i2 when we come to ,no4 #aj tree1 it must have the same as one of the other trees1 as it could not have #aj or more according to our first supposition4 7#aad7 ,it simply means that four 8nothings0 equal one 8nothing40 7#aae7 ,he had a half-penny1 and he borrowed a half-penny4 7#aaf7 #e4 7#aag7 #cj apples4 7#aah7 #ah and #bg4 7#aai7 ,a #cbdj ,b #biaf ,c #aidd ,d #bjeb ,e #agbh ,electors #fdhj4 7#abj7 ,a #ab ,b #bj ,c #cj 7#aba7 #de miles4 7#abb7 #hj1 #fj1 #de4 7#abc7 #ehj4 7#abd7 ,hendrick and ,anna4 ,claas and ,catrn4 ,cornelius and ,gertruig4 7#abe7 ,a #bcjd ,b #abif 7#abf7 #ai1jje4 7#abg7 #ae days4 7#abh7 #ast #bahj #cs4 #d;d4 #bnd #bchj #aes4 #aa;d4 #crd #beii #ags4 #i;d4 #dth #bhci #bs4 #aj;d4 7#abi7 #a-b_/ah minutes4 7#acj7 #cf pyramids4 7#aca7 #hbjgf feet4 7#acb7 #ee-e_/e #ef #d x #d plus #dj4 7#acc7 #f women4 #aj;d4 per yard4 7#acd7 ,a #ba4 ,b #bh4 ,youngest child #g4 7#ace7 ,we see that each of the members present paid #d;d4 to make up #es4 ,there must have been #ae persons present when the bill was paid1 and consequently #ah at dinner4 ,now1 it is evident that the classes are as #b1 #c1 and #d1 making #d ,officers1 #f ,non-com's1 and #h ,privates4 ,again1 it is evident that #es4 being the sum to be paid by #a ,com4 and #b ,non-coms42 each ,com4's share was #bs41 and each ,non-com's #as4 #f;d41 and from the conditions of the question each ,private's share was #as4 #c;d42 those who remained had to pay4 #c ,officers1 #bs4 each and #d;d4 each #gs4 #j;d4 #d ,non-coms1 #as4 #f;d4 each #gs4 #d;d4 #h ,privates1 #as4 #c;d4 #abs4 #h;d4 ----------- ,amount #a #gs4 #j;d4 7#acf7 ,the ,alphabet4 7#acg7 #d glasses4 7#ach7 #cgfiib feet4 7#aci7 #aeg-a_/g square miles4 7#adj7 #cbd4 7#ada7 ,bottle #b;d41 cork d4 7#adb7 #a1 #d1 #af1 and #fd4 7#adc7 #af days4 7#add7 #g;d41 #d;d4 7#ade7 #ast1 #fd2 #bnd1 #dh2 #crd1 #cf2 #dth1 #bg gals4 7#adf7 #ast #bd1 #bnd #bj1 #crd #h1 #dth #bh4 7#adg7 ,this is one of those impossible questions that one often hears4 ,the fractions1 when added together1 equal #ai_/bj4 ,so the whole #a cannot be so divided4 ,the following solution is often put forward3-- plus plus plus #bj plus #ae plus #ab plus #aj #eg -------------------------- -- #fj #fj s4 #bj x #bj #djj div4 #eg #g-a_/eg to #ast son #ae x #bj #cjj div4 #eg #e-ae_/eg #bnd #ab x #bj #bdj div4 #eg #d-ab_/eg #crd #aj x #bj #bjj div4 #eg #c-bi_/eg #dth -------- #bjs4 7#adh7 ,the locomotive pushes ,no4 #a truck up to the points1 then returns to the opposite siding and pushes ,no4 #b up to ,no4 #a at the points2 the two trucks are then pulled by the locomotive down the siding and pushed on to the main line to a position anywhere between the two sidings2 ,no4 #a is then uncoupled and left standing1 whilst the locomotive pulls ,no4 #b along the main line in order to push it up to the points where it is left2 the locomotive returns to ,no4 #a1 and pulling it a short distance1 in order to get on the proper siding1 pushes it into its required position1 uncouples1 and proceeds up the other siding to the points to pull ,no4 #b into its proper place1 then uncouples and returns to the main line4 7#adi7 #ad1djj quarts 7#aej7 ,a1 #bs4 #g;d42 ,b1 #as4 #a;d42 ,c1 #i;d4 7#aea7 #ast ,company1 #bdjj #bnd #ahjj #crd #afjj #dth #aejj ----- #gcjj 7#aeb7 ,lines1 #bi2 letters1 #cb4 7#aec7 ,major #ajj1 minor #fj4 7#aed7 ,from ,a #hh1 from ,b #dd4 7#aee7 ,illustration 7#aef7 #be miles from ,sydney4 7#aeg7 #d miles4 7#aeh7 #ajh4 7#aei7 ,two-thirds of ,,six is ,,ix2 the upper half of ,,xii is ,,vii2 ,the half of ,,five is ,,iv2 and the upper half of ,,xi is ,,vi4 7#afj7 #ab #abs4 #h;d4 #ababh farthings4 7#afa7 ,j #ffj1 ,m #ddj1 ,b #bbj4 7#afb7 ,masons #bjs41 ,bricklayers #aes41 ,laborers #ajs4 7#afc7 #bi #ais4 #i;d4 7#afd7 #b years4 7#afe7 ,illustration ,this draught puzzle can also be done in three other ways4 7#aff7 ,wife #dfej ,son #fbjj ,eldest daughter #cajj ,youngest #aeej ------ ,total #ae1ejj 7#afg7 ,illustration 7#afh7 #ah4 7#afi7 #f per cent4 7#agj7 #ai movements #ai feet 7#aga7 #hie and #aa1bgg4 7#agb7 #ef quarts4 7#agc7 #bj2 #ej gals4 7#agd7 #aag ft4 #i in4 7#age7 #ast #a;d41 #bnd d4 7#agf7 ,the lazy sundowner #b days at #b hours per day #d hours second #d #d #af third #f #f #cf fourth #ab #ab #add -------- #bjj hours 7#agg7 #agggghgc4 7#agh7 ,the 8catch0 is in the word ears2 he carries out two ears on his head and one ear of corn each day--hence it will take #f days4 7#agi7 ,my daughter4 7#ahj7 ,man #cs41 boy #bs4 7#aha7 #aai4 7#ahb7 #gb gals4 7#ahc7 ,the landlord would lose by such an arrangement1 as the rent would entitle him to #b_/e of the #ah2 the selector should give him #ah bushels from his own share after the division is completed4 7#ahd7 #a #fs4 #h;d41 #a #acs4 #d;d4 7#ahe7 #c4cfb inches4 7#ahf7 ,the merchant1 #a;d4 7#ahg7 ,train from ,london #dd miles per hour ,edinburgh #ec-g_/i 7#ahh7 ,a gentleman and one servant go over2 the gentleman returns with the boat1 #b servants go over2 #a servant returns2 #b gentlemen go over2 #a gentleman and #a servant return2 #b gentlemen go over2 #a servant returns2 #b servants go over2 #a servant returns2 the two servants then go over4 7#ahi7 ,imperfect4 7,sample of questions we receive daily4 ,give it to your friends3 it will annoy them47 7#aij7 #ad1 #aab1 #cgh1 #hif4 7#aia7 #abj lbs4 7#aib7 #hj years4 7#aic7 #f-f_/f4 7#aid7 #ac trains4 7#aie7 ,distance1 #ab miles2 rate1 #h miles per hour4 7#aif7 #e hours4 7#aig7 ,a #cis41 ,b #bas41 ,c #abs4 7#aih7 #aj4 7#aii7 ,when ,pharaoh's daughter drew a little prophet 7profit7 from the banks of the ,nile4 7#bjj7 #dlbs4 7#bja7 ,illustration 7#bjb7 #cj oz4 of #ba1 #ij oz4 of #bc4 7#bjc7 #a #bs4 #b;d4 7#bjd7 #cjgh ac4 #cr4 #bhhp4 7#bje7 #ajh trees4 7#bjf7 #gib4 7#bjg7 ,illustration 7#bjh7 #h_/ej4 7#bji7 #gb inches4 7#baj7 #ii-i_/i4 7#baa7 ,a #e1 ,b #g4 ,,the ,,brick ,,puzzle4 7#bab7 #b stretchers1 #d headers1 #d closures4 ,area1 #ace inches4 ,this question has been the cause of much discussion1 especially amongst those engaged in the building trade4 ,illustration3 ,fig4 #a--,represents the brick and the method of cutting it4 ,illustration3 ,fig4 #b--,represents the face of the wall showing the area of brick when cut4 ,it has been necessary to produce this figure on half-scale to that of ,fig4 #a4 7#bac7 ,goose #cj1 duck #ej1 hen #gj4 ,,the ,,knight ,,move4 7#bad7 ,it does not matter on which square the knight is first placed1 his last square to enter will be at a knight's distance from the first4 ,the route may be varied in many ways4 ,illustration 7#bae7 #b4 7#baf7 ,a #c1 ,b #f1 ,c #ah4 7#bag7 ,cannot be answered4 7#bah7 ------------------ #h #bef #b ------------------ #d #af #fd ------------------ #abh #a #cb ------------------ 7#bai7 ,even1 #f against #f--ab #b to #a1 #h against #d--ab #c to #a1 #i against #c--ab -- #ac ,received4 ,whichever horse wins1 he must pay #ab1 and has received #ac to pay with4 7#bbj7 #h4 7#bba7 #i to #h on4 7#bbb7 #a lb4 of feathers by #abdj grains2 #a oz4 of gold by #dbe grains4 7#bbc7 ,illustration 7#bbd7 ,sovereigns1 #d2 half-crowns1 #h4 7#bbe7 ,count backwards1 saying #bj1 #ai1 #ah1 #ag1 with emphasis on the #ag1 remarking 8,that's odd1 isn't it80 ,the reply will be 8,yes40 ,proceed in that manner throughout4 ,this question and ,no4 #f1 although not the best of 8catches10 are often asked4 7#bbf7 ,,six ,,ix ,,xl ,,ix ,x ,l ----------- ,s ,i ,x 7#bbg7 ,man #bd1 woman #af4 7#bbh7 #gb miles4 7#bbi7 ,the diameter of the earth4 7#bcj7 #dbj4 7#bca7 #jjjjaaegd4 7#bcb7 #ah seconds4 7#bcc7 #aidje inches4 7#bcd7 ,illustration ,he must cut the piece of veneer as shown by the middle figure1 when he will be able to get his two ovals4 7#bce7 ,because you double it when you put it in your pocket1 and you see it in creases 7increases7 when you take it out4 7#bcf7 ,he did this in two ways2-- ,table ,full4 ,half-full4 ,empty4 #a #b #c #b #b #b #c #b #c #c #a #c ------------------------------------ #a #c #a #c #b #c #a #c #c #a #e #a 7#bdb7 ,illustration 7#bdc7 #g #g #f #g #e #d #c #b #a 7#bdd7 #ahj4 7#bde7 ,worked #bg days1 idle #cc4 7#bdf7 ,,xix1 take away ,i1 leaves ,,xx4 7#bdg7 ,the ,cadi added his camel to the #ag1 thus making #ah in all2 then the oldest son received #i1 second son #f1 youngest #b4 ,he then took his own camel1 and1 departing1 left the sons quite satisfied4 7#bdh7 #b1 #d1 #h1 #af1 #cb1 #fd lbs4 7#bdi7 #ac horses1 #bf cattle1 #ci pigs4 7#bej7 #ab ft4 #aa in4 7#bea7 #ast boy1 #adah farthings #bnd #chb 7#beb7 ,jack1 #aj yrs4 ,tom ,,five ,tom ,five ,james1 #i ,bob ,six ,bob ,six ,fred1 #h ,jack ,ten ,fred ,eight ,bob1 #f ,baby ,one ,jack ,ten ,tom1 #e ,james ,nine ,baby ,one ,baby1 #a ,fred ,eight ,james ,nine 7#bec7 #gibf feet4 7#bed7 #i plus #i plus #i plus #c #cj1 #ci-i_/i #dj1 or #bh-b_/a #cj1 #bh plus #ab #dj4 7#bee7 #e;d4 7#bef7 #aifjghdcacgbedi4 ,method3 ,keep on adding imaginary #c's until it comes out thus--#ag7cc_/ag7aifjghdcacgbedi ,to prove it3-- #aifjghdcacgbedi #ag ---------------- ,proof-- #cccccccccccccccc 7#beg7 #bh eggs4 ,method3 #a hens lay #a eggs in #a days #a #c #c #c #f #c #c #b #a #f #d #a #f #bh #g 7#beh7 ,tom1 #ds4 #f;d4 per day2 ,bill1 #cs4 7#bei7 #ajjj4 7#bfj7 #a inch remainder4 7#bfa7 ,illustration 7#bfb7 #cic1bac shillings4 7#bfc7 #b_/i4 7#bfd7 #i4 7#bfe7 #d seconds4 7#bff7 ,loses #ej4 7#bfg7 ,he will never enter the water1 because the frog's jump1 at any time1 is only half-way to the water4 7#bfh7 ,illustration 7#bfi7 #a minutes4 7#bgj7 #di years4 7#bga7 #c minutes4 7#bgb7 --------------------------------- ,a ,b ,c ,d ,e ,let ,a be starting point of ,orderly2 ,b be starting point of ,general2 ,c be point at which ,orderly returns to his place1 the rear having marched #ej miles to this point2 ,d be point at which ,orderly delivers his despatches2 ,e be destination of front rank or ,general of ,army4 ,let x eq4 number of miles between ,c and ,d4 ,then ,,ad eq4 7#ej plus x7 miles2 ,,bd eq4 7#be plus x7 miles2 ,,de eq4 7#be minus x7 miles2 and ,,ad plus ,,dc eq4 7#ej plus #bx7 miles1 and is the total distance the ,orderly travels4 ,now ,orderly rides from ,a to ,d1 while ,general marches from ,b to ,d1 and ,orderly returns from ,d to ,c1 while ,general marches from ,d to ,e1 and ,orderly and ,army travel at a uniform rate4 ,,ad 3 ,,bd 33 ,,dc 3 ,,de or #ej plus x 3 #be plus x 33 x 3 #be-x #abej-bex-x#b eq4 #bex plus x#b ,whence x eq4 #ae4de plus4 ,orderly rides #ej plus #cj4i plus eq4 #hj4i plus eq4 #hj miles #aehg yards nearly4 7#bgc7 #djj lbs4 7#bgd7 ,gentleman #cj1 boy #ae4 7#bge7 ,ride1 #dd miles2 area1 #gg1ddj acres4 7#bgf7 ,translation3 ,the foundation stone of this building was laid in #ahhj by ,sir ,charles ,lilley1 for many years ,chief ,justice1 and formerly a distinguished member of the ,government of this colony4 ,he was prominent amongst those who worked for the first establishment of this school1 and afterwards1 by his generous gifts and by his wise counsel as a trustee1 contributed greatly to its advancement4 ,the trustees have1 therefore1 erected this tablet to perpetuate his memory here4 ,a4,d4 #ahih4 7#bgg7 ,the agent owes the firm #g #ais4 ,,diddams ,,printer1 ,,brisbane4