If first my age is multiplied by three,And then of that two-sevenths tripled be,The square root of two-ninths of this is four;Now tell my age, or never see me more—
If first my age is multiplied by three,And then of that two-sevenths tripled be,The square root of two-ninths of this is four;Now tell my age, or never see me more—
If first my age is multiplied by three,And then of that two-sevenths tripled be,The square root of two-ninths of this is four;Now tell my age, or never see me more—
she was 28 years old.
Back to Description
If cars run, at uniform speed, from Shepherd’s Bush to the Bank, at intervals of two minutes, and I am travelling at the samerate in the opposite direction, I shall meet 30 in half-an-hour, for there are already 15 on the track approaching me, and 15 are started from the other end during my half hour’s course.
Back to Description
If it was possible to carry out my offer of a farthing for every different group of apples which my greengrocer could select from a basket of 100 apples, he would be entitled to the stupendous sum of £18,031,572,350 19s. 2d.
Back to Description
If the minute-hand of a clock moves round between 3 and 4 in the opposite direction to the hour-hand, the hands will be exactly together when it is really 417â„13minutes past 3.
Back to Description
If the walnut monkey had stopped to help the other, and they had eaten filberts at equal rates, they would have escaped in 21â„4minutes.
Back to Description
The value of the cheque, for which the cashier paid by mistake pounds for shillings, was £5, 11s. 6d. The receiver to whom £11, 5s. 6d. was handed, spent half-a-crown, and then found that he had left £11, 3s., just twice the amount of the original cheque.
Back to Description
The number 14 can be made up by adding together five uneven figures thus:—11 + 1 + 1 + 1. It will be seen that although only fournumbersare used, 11 is made up oftwo figures.
Here is another, and quite a curious solution, 1 + 1 + 1 + 1 = 4, and with another 1 we can make up 14!
Back to Description
A business manager can fill up three vacant posts of varying value from seven applicants in 210 different ways. For the firstpost there would be a choice among 7, for the second among 6, and for the third among 5, so that the possible variations would amount to 7 × 6 × 5 = 210.
Back to Description
If the fasting man, who began his task at noon, said it is now5â„11of the time to midnight, he spoke at 3.45 p.m., meaning that5â„11of the remaining time till midnight had elapsed since noon.
Back to Description
If a clock takes six seconds to strike 6, it will take 12 seconds to strike 11, for there must be ten intervals of 11â„5seconds each.
Back to Description
Twenty horses can be arranged in three stalls, so that there is an odd number in each, by placing one in the first stall, three in the second, and sixteen (an odd number to put into any stall!) in the third.
Back to Description
The little problem, “Givena,b,c, to findq,†is solved, without recourse to algebra, thus:a,b,c, =c,a,b; take a cab and go over Kew Bridge, and you find a phoneticQ!
Back to Description
Tom Evergreen was 75 years old when he was asked his age by some men at his club in 1875, and said—“The number of months that I have lived are exactly half as many as the number which denotes the year in which I was born.â€
Back to Description
Eight different circles can be drawn. A circle can have one of the three inside and two outside in three ways, or one outside and three inside in three ways (each of the three being inside or outside in turn), or all three may be inside, or all three may be outside, the touching circle.
Back to Description
The way to arrange 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, so that used once each they form a sum which is equal to 1 isthis:—
3570+148296= 1
Back to Description
The sum of the first fifty numbers may be found without any addition thus:—The first fifty numbers form twenty-five pairs of fifty-one each (1 + 50, 2 + 49, etc., etc.), and 51 × 25 is practically 51 × 100 ÷ 4 = 1275.
Back to Description
The tramcarA, which started at the same time asB, but ran into a “lie by†in four minutes, and waited there five minutes tillBcame along, when they completed their courses at the same moment in opposite directions, could have run the whole distance in ten minutes.
Back to Description
What remains will be 8 if we take 10 and double it by writing one 10 over another so as to form 18, and then deduct 10.
Back to Description
If the average weight of the Oxford crew is increased by 2â„”s., when one of them who weighs 12 stone, is replaced by a fresh man, the weight of that substitute is 13 stone 2â„”s.
Back to Description
If a motor-car is twice as old as its tyres were when it was old as its tyres are, and if, when these tyres are as old as the car itself is now, their united ages will be 21â„4years, the car is now 12 months old, and the tyres have had 9 months’ wear.
Back to Description
AandB, who could each carry provisions for himself for twelve days, started to penetrate as far as possible into a desert, on the understanding that neither of them should miss a day’s food. After an advance of four days, each had provisions still for eight days. One gave four portions of his store to his companion, which did not overload him, and returned with the other four. His comrade was then able to advance another four days’ journey, and still have rations for the eight days’ return. Thus the furthest possible penetration into the desert under the conditions was an eight days’ march.
Back to Description
If, when a bottle of medicine and its cork cost half-a-crown, the bottle and the medicine cost two and a penny more than the cork, the cork cost twopence half-penny.
Back to Description
A boat’s crew far from land, with no sail or oars, and with no assistance from wind or stream, or outside help of any kind, can regain the shore by means of a coil of rope. Motion is given to the boat by tying one end of the rope to the after thwart, and giving the other end a series of violent jerks in a direction parallel to the keel. This curious illustration of mechanical principles is from “Ball’s Mechanical Recreations.†(Macmillan.)
Back to Description
It will be found that after a crown and as many four-shilling pieces as possible have been crammed into our pockets, there would still be room for one sixpence and one threepenny-piece in some corner or cranny. We can, therefore, have one crown, one sixpence, one threepenny-piece, and as many four-shilling pieces as our pockets will hold, and yet be unable to give change for a half-sovereign.
Back to Description
There were fifteen apples in the basket. Half of these and half an apple,i.e., eight were first given, then half the remainder and half an apple,i.e., four, then on similar lines two, leaving one in the basket.
Back to Description
The QueerDivision—
A third of twelve divideBy just a fifth of seven;And you will soon decideThat this must give eleven—
A third of twelve divideBy just a fifth of seven;And you will soon decideThat this must give eleven—
A third of twelve divideBy just a fifth of seven;And you will soon decideThat this must give eleven—
is solved by LV ÷ V, or 55 ÷ 5 = 11.
Back to Description
A motor that goes 9 miles an hour uphill, 18 miles an hour downhill, and 12 miles an hour on the level, will take 8 hours and 20 minutes to run 50 miles out and return at once over the same course.
Back to Description
The number of shots fired at a mark was 420 each byA,B, andC.Amade 280 hits,B315, andC336.
Back to Description
If a dog and a cat, evenly matched in speed, run a race out and back over a course of 75 yards in all, and the dog always takes 5 feet at a bound, and the cat 3 feet, the cat will win, because at the turning point the dog overleaps the half distance more than the cat does, and so has a longer run in.
Back to Description
When a man caught up a wagon going at 3 miles an hour, which was just visible to him in a fog at a distance of 55 yards, and which he saw for five minutes before reaching it, he was walking at the rate of 33â„8miles an hour.
Back to Description
Three horses,A B C, can be placed after a race in thirteen different ways, thus:—A B C,A C B,B A C,B C A,C A B,C B A, orA B Cas a dead heat; orA B,A C, orB Cequal for the first place; orAfirst withB Cequal seconds; orBfirst withA Cequal seconds; orCfirst withA Bequal seconds.
Back to Description
The 34 points scored against Oxbridge by the New Zealanders can be made up in two ways, either by 8 tries and 2 converted tries, or by 3 tries and 5 converted tries.
The highest possible score on these lines is 10 tries converted, equalling 50 points, and as the New Zealanders’ score, if all tries are converted, becomes four-fifths of this, their actual score was 3 tries and 5 converted into goals.
Back to Description
The smallest number, of which the alternate figures are cyphers, which is divisible by 9 and by 11 is 909090909090909090909!
Back to Description
Our problem in which it is stated thatAwith 8d. metBandCwith five and three loaves, and asked how the cash should be divided betweenBandC, if all agreed to share the loaves. Now each eats two loaves and two-thirds of a loaf, andBgives seven-thirds of a loaf toA, whileCgives him one-third of a loaf. SoBreceives 7d. andC1d.
Back to Description
When, on opening four money-boxes containing pennies only, it was found that those in the first with half of all the rest, those in the second with a third of the others, those in the third with a fourth, and those in the fourth with a fifth of all the rest, amounted in each case to 740, the four boxes held £6. 1s. 8d., and the numbers of pennies were 20, 380, 500, and 560.
Back to Description
If two steamers,AandB, start together for a trip to a distant buoy and back, andAsteams all the time at ten knots an hour, whileBgoes outward at eight knots and returns at twelve knots an hour,Bwill regain port later thanA, because its loss on the outward course will not have been recovered on the run home.
Back to Description
If in London a new head to a golf club costs four times as much as a new leather face, while at St Andrews it costs five times as much, and if the leather face costs twice as much in London as in St Andrews, and if, including a shilling paid for a ball, the charges in London were twice as much as they would have been at St Andrews, the London cost of a new head is four shillings, and of a leather face a shilling.
Back to Description
When two children were asked to give the total number of sheep and cattle in a pasture, from the number of each sort, and one by subtraction answered 10, while the other arrived at 11,900 by multiplication, the true numbers were 170 sheep, 70 cattle, 240 in all.
Back to Description
If a man picks up one by one fifty-two stones, placed at such intervals on a straight road that the second is a yard from the first, the third 3 yards from the second, and so on with intervals increasing each time by 2 yards, and bring them all to a basket placed at the first stone, he has to travel about 52 miles, or, to be quite exact, 51 miles, 1292 yards.
Back to Description
When, in the House of Commons, if the Ayes had been increased by 50 from the Noes, the motion would have been carried by 5 to 3;and if the Noes had taken 60 votes from the Ayes it would have been lost by 4 to 3, the motion succeeded; 300 voted “Aye,†and 260 “No.â€
Back to Description
There are 143 positions on the face of a watch in which the places of the hour and minute-hands can be interchanged, and still indicate a possible time. There would be 144 such positions but for the fact that at twelve o’clock the hands occupy the same place.
Back to Description
If in a cricket match the scores in each successive innings are a quarter less than in the preceding innings, and the side which goes in first wins by 50 runs, the complete scores of the winners are 128 and 72, and of the losers 96 and 54.
Back to Description
When a ball is thrown vertically upwards, and caught five seconds later, it has risen 100 feet. It takes the same time to rise as to fall, and when a body falls from rest, it travels a number of feet represented by sixteen times the square of the time in seconds.
Hence comes the rule that the height in feet of a vertical throw is found by squaring the time in seconds of its flight, and multiplying by four.
Back to Description
The carpet which, had it been 5 feet broader and 4 feet longer, would have contained 116 more feet, and if 4 feet broader and 5 longer 113 more, was 12 feet long and 9 feet broad.
Back to Description
When, in estimating the cost of a hundred similar articles, shillings were read as pounds, and pence as shillings, and the estimated cost was in consequence £212, 18s. 4d. in excess of the real cost, the true cost of each article was 2s. 5d.
Back to Description
If the square of the number of my house is equal to the difference of the squares of the numbers of my next door neighbours’ houses, and if my brother in the next street can say the same of his house, though its number is not the same as that of mine, our houses are numbered 8 and 4. In my street the even numbers are all on one side, in my brother’s street they, run odd and even consecutively, and so 82= 102- 62, and 42= 52- 32.
Back to Description
When two men of unequal strength have to move a block which weighs 270 â„”s., on a light plank 6 feet long, if the stronger man can carry 180 â„”s., the block must be placed 2 feet from him, so that he may have that share of the load.
Back to Description
If a man who had twenty coins, some shillings, and the rest half-crowns, were to change the half-crowns for sixpences, and the shillings for pence, and then found that he had 156 coins, he must have had eight shillings at first.
Back to Description
If, when coins are placed on a table at equal distances apart, so as to form sides of an equilateral triangle, and when as many are taken from the middle of each side as equal the square root of the number on that side, and placed on the opposite corner, the number on each side is then to the original number as five is to four, there are forty-five coins in all.
Back to Description
When the gardener found that he would have 150 too few if he set his posts a foot apart, and seventy to spare if he set them at every yard, he had 180 posts.
Back to Description
In order to buy with £100 a hundred animals, cows at £5, sheep at £1, and geese at 1s. each, the purchaser must secure nineteen cows, one sheep, and eighty geese.
Back to Description
If John, who is 21, is twice as old as Mary was when he was as old as Mary is, Mary’s age now is 153â„4years.
Back to Description
If in a cricket matchAmakes 35 runs, andCandDmake respectively half and a third ofB’s score, and ifBscores as many less thanAasCscores more thanD,Bmade 30,C15, andD10 runs.
Back to Description
The least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10, leaves remainders 1, 2, 3, 4, 5, 6, 7, 8, 9, is 2519, their least common multiple less 1.
Back to Description
A square table standing on four legs, which are set at the middle points of its sides, can at most uphold its own weight upon one of its corners.
Back to Description
The division of ninety-nine pennies, so that share 1 exceeds share 2 by 3, is less than share 3 by 10, exceeds share 4 by 9, and is less than share 5 by 16, is 17, 14, 27, 8, and 33.
Back to Description
If Indians carried off a third of a flock and a third of a sheep, and others took a fourth of the remainder and a fourth of a sheep, and others a fifth of the rest and three-fifths of a sheep, and there were then 409 left, the full flock was 1025 sheep.
Back to Description
When a cistern which held fifty-three gallons was filled by three boys,Abringing a pint every three minutes,Ba quart every five minutes, andCa gallon every seven minutes, it took 230 minutes to fill it, andBpoured in the final quart,AandCcoming up one minute too lateto contribute at the last.
Back to Description
A man who said, late in the last century, that his age then was the square root of the year in which he was born, was speaking in the year 1892.
Back to Description
If when a dealer in curios sold a vase for £119, his profit per cent., and the cost price of the vase, were expressed by the same number, it had cost him £70.
Back to Description
The chance of throwing at least one ace in a single throw with a pair of dice is11â„36, for there are five ways in which each dice can be thrown so as not to give an ace, so that twenty-five possible throws exclude aces. Hence the chance ofnotthrowing an ace is25â„36, which leaves11â„36in favour of it.
Back to Description
The policeman who ran after a thief starting four minutes later, and running one-third faster, if they both ran straight along the road, caught him in twelve minutes.
Back to Description
At a bazaar stall, where twenty-seven articles are exposed for sale, a purchaser may buy one thing or more, and the number of choices open to him is one less than the continued product of twenty-seven twos, or 134217727.
Back to Description
168. When Nellie’s fathersaid:—
I was twice as old as you areThe day that you were born.You will be just what I was thenWhen fourteen years are gone—
I was twice as old as you areThe day that you were born.You will be just what I was thenWhen fourteen years are gone—
I was twice as old as you areThe day that you were born.You will be just what I was thenWhen fourteen years are gone—
he was 42, and she was 14.
Back to Description
The word square is completedthus:—
Back to Puzzle
The word square filled inis:—
Notice the curious diagonal of E’s.
Back to Puzzle
In the incomplete sentence,
SO * * * * AG * * * * LATI * * * * X * * * * ITH
the duplicate letters are filled inthus:—
SOME MEAGRE RELATIVE VEXED EDITH
The two last letters of each word are repeated as the two first of the word that follows.
Back to Puzzle
The word square is completedthus:—
Back to Puzzle
By twice building up two Ds into a B we make BULBOUS.
Back to Puzzle
The question put on paper to the love-lorn youth, “Loruve?†is, when interpreted, “Are you in love?†and the advice given to him on another slip, “ProveLA  FDand ensure success,†reads into, “Prove a fond lover, and ensure success†(a fond lover).
Back to Puzzle
Back to Puzzle
The completed word squareis—
Back to Puzzle
The oracular response to a young Frenchman at afête, who inquired how he could best please theladies—
MEC DO BIC
conceals this sageadvice—
Aimez, cédez, obéissez!Love, yield, obey!
Aimez, cédez, obéissez!Love, yield, obey!
Aimez, cédez, obéissez!Love, yield, obey!
Back to Puzzle
The solution to our Letter Fraction Problem is of a verbal character. The original statement
moty=Â mo
is dealt withthus:—
monotony = monot ony, and so the word monotony solves the equation.
Back to Puzzle
The buried beasts arechamois,buffalo,heifer, andleopard; and when the Oxford athletecries—
“Though I jump and row and run,Cap or cup I never wonâ€
“Though I jump and row and run,Cap or cup I never wonâ€
“Though I jump and row and run,Cap or cup I never wonâ€
he introduces us to aporcupine.
Back to Puzzle
Thelines—