NUTS TO CRACK
103. I bought a parcel of nuts at forty-nine for twopence. I divided it into two equal parts, one of which I sold at twenty-four, the other at twenty-five for a penny. I spent and received an integral number of pence, but bought the least possible number of nuts. How many did I buy? What did they cost? What did I gain?
MONEY MATTERS
104. My purse contained sovereigns and shillings. After I had spent half of its contents there were as many pounds left as I had shillings at first. With what sum did I start?
A DELICATE QUESTION
105. A lady was asked her age in a letter, and she replied by postcard thus:—
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!
What was her age?
106.
If cars run at uniform speed on the twopenny tube, from Shepherd’s Bush to the Bank at intervals of two minutes, how many shall I meet in half an hour if I am travelling from the Bank to Shepherd’s Bush?
PAYMENT BY RESULTS
107. What would it cost me to keep my word if I were to offer my greengrocer a farthing for every different group of ten apples he could select from a basket of a hundred apples?
108.
If the minute-hand of a clock moves round in the opposite direction to the hour-hand, what will be the real time between three and four, when the hands are exactly together?
109.
Two monkeys have stolen some filberts and some walnuts. As they begin their feast they see the owner of the garden coming with a stick. It will take him two and a half minutes to reach them. There are twice as many filberts as walnuts, and one monkey finishes the walnuts at the rate of fifteen a minute in four-fifths of the time and bolts. The other manages to finish the filberts just in time.
If the walnut monkey had stopped to help him till all was finished, when would they have got away if they ate filberts at equal rates?
110.
A cashier, in payment for a cheque, gives by mistake pounds for shillings and shillings for pounds. The receiver spends half-a-crown, and then finds that he has twice as much as the cheque was worth. What was its value?
111.
What five uneven figures can be added together so as to make up 14?
112.
Three posts which vary in value are vacant in an office. In how many ways can the manager fill these up from seven clerks who apply for the appointments?
113.
“It is now 5⁄11 of the time to midnight,” said the fasting man, who began his task at noon. What time was it?
A STRIKING TIME
114. If a clock takes six seconds to strike six how long will it take to strike eleven?
WHAT ARE THE ODDS?
115. How would you arrange twenty horses in three stalls so as to have an odd number of horses in each stall?
116.
Here is a pretty little problem, which has at any rate an Algebraic form, and is exceedingly ingenious:—
Given a, b, c, to find q.
WHEN WAS HE BORN?
117. Tom Evergreen was asked his age by some men at his club on his birthday in 1875. “The number of months,” he said, “that I have lived are exactly half as many as the number which denotes the year in which I was born.” How old was he?
118.
Draw three circles of any size, and in any position, so long as they do not intersect, or lie one within another. How many different circles can be drawn touching all the three?
119.
We have seen that the nine digits can be so dealt with, using each once, as to add up to 100. How can 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 be arranged so that they form a sum which is equal to 1?
120.
How is it possible, by quite a simple method, to find the sum of the first fifty numbers without actually adding them together?
121.
Two tram-cars, A and B, start at the same time. A runs into a “lie by” in four minutes, and waits there five minutes, when B meets and passes it. Both complete the whole course at the same moment. In what time can A complete it without a rest?
A CURIOUS DEDUCTION
122. Take 10, double it, deduct 10, and tell me what remains.
123.
The average weight of the Oxford crew is increased by 2 lbs., when one of them, who weighs 12 stone, is replaced by a fresh man. What is the fresh man’s weight?
ASK ANY MOTORIST
124. A motor car is twice as old as its tyres were when it was as old as its tyres are. When these tyres are as old as the car is now, the united ages of car and tyres will be two years and a quarter. What are their respective ages now?
125.
A and B on the edge of a desert can each carry provisions for himself for twelve days. How far into the desert can an advance be made, so that neither of them misses a day’s food?
126.
A bottle of medicine and its cork cost half-a-crown, but the bottle and the medicine cost two shillings and a penny more than the cork. What did the cork cost?
IN A FIX
127. A boat’s crew are afloat far from land with no sail or oars. How can they, without making any use of wind or stream, and without any outside help, regain the shore by means of a coil of rope which happens to be at hand.
128.
What is the largest sum in silver that I can have in my pockets without being able to give change for a half-sovereign.
129.
I have apples in a basket. Without cutting an apple I give half of the number and half an apple to one person; half of what then remains and half an apple to another, and half of what are still left and half an apple to a third. One apple now remains in the basket. How many were there at first?
A QUEER DIVISION
130.
A third of twelve divide
By just a fifth of seven;
And you will soon decide
That this must give eleven.
131.
A motor goes 9 miles an hour uphill, 18 miles an hour downhill, and 12 miles an hour on the level. How long will it take to run 50 miles and return at once over the same course?
132.
In firing at a mark A hits it in two out of three shots, B in three out of four, and C in four out of five. The mark was hit 931 times. If each fired the same number of shots, how many hits did each make, and how many shots were fired?
133.
If a cat and a dog, evenly matched in speed, run a race out and back over a course 75 yards in all, and the dog always takes 5 feet at a bound and the cat 3 feet, which will win?
IN A FOG
134. In a fog a man caught up a wagon going in the same direction at 3 miles an hour. If the wagon was just visible to him at a distance of 55 yards, and he could see it for five minutes, at how many miles an hour was he walking?
135.
Three horses start in a race. In how many different ways can they be placed by the judge?
NEW ZEALAND FOOTBALL
136. The New Zealanders, winning a match against Oxbridge, scored 34 points, from tries and tries converted into goals.
If every try had been converted they would have made four-fifths of the maximum which a score of 34 points from tries and goals can yield.
What is this maximum, and what was their actual score?
137.
What is the smallest number, of which the alternate figures are cyphers, that is divisible by 9 and by 11?
138.
Here is an interesting little problem:—A, with 8d. in his hand, meets B and C, who have five and three loaves respectively. In hungry mood they all agree to share the loaves equally, and to divide the money fairly between B and C. How much does each receive?
THE MONEY-BOXES
139. When four money-boxes, containing pennies only, were opened and counted, it was found that the number in the first with half those in all the others, in the second with a third of all the others, in the third with a fourth of all the others, and in the fourth with a fifth of all the others, amounted in each case to 740. How much money did the boxes contain, and how was it divided?
140.
Two steamers start together to make a trip to a far-off buoy and back. Steamer A runs all the time at 10 miles an hour. Steamer B does the passage out at 8 miles an hour, and the return at 12 miles. Will they regain port together?
141.
A golf player has two clubs mended in London. One has a new head, the other a new leather face. The head costs four times as much as the face. At St Andrews it costs five times as much, and the leather face at St Andrews is half the London price. Including a shilling for a ball he pays twice the St Andrews charges for these repairs. What is the London charge for each?
FROM TWO WRONGS TO MAKE A RIGHT
142. Two children were asked to give the total number of animals in a pasture, where sheep and cattle were grazing. They were told the numbers of sheep and of cattle, but one subtracted, and gave 100 as the answer, and the other arrived at 11,900 by multiplication. What was the correct total?
THE STONE CARRIER
143. Fifty-two stones are placed at intervals along a straight road. The distance between the first and the second is 1 yard, between the second and the third it is 3 yards, between the next two 5 yards, and so on, the intervals increasing each time by 2 yards.
How far would a tramp have to travel to earn five shillings promised to him when he had brought them one by one to a basket placed at the first stone?
144.
On a division in the House of Commons, if the Ayes had been increased by fifty from the Noes, the motion would have been carried by five to three. If the Noes had received sixty votes from the Ayes, it would have been lost by four to three. Did the motion succeed? How many voted?
A WATCH PUZZLE
145. How many positions are there on the face of a watch in which the places of the hour and minute-hands can be interchanged so as still to indicate a possible time?
CRICKET SCORES
146. In a cricket match the scores in each successive innings are a quarter less than in the preceding innings. The match was played out, and the side that went in first won by fifty runs. What was the complete score?
HOW HIGH CAN YOU THROW?
147. A boy throws a cricket ball vertically upwards, and catches it as it falls just five seconds later. How high from his hands does the ball go?
MEASURE THE CARPET
148. It may be said of a section of the gigantic carpet at Olympia that had it been 5 feet broader and 4 feet longer it would have contained 116 more feet; but if 4 feet broader and 5 longer the increase would have been but 113 feet. What were its actual breadth and length?
149.
In estimating the cost of a hundred similar articles, the mistake was made of reading pounds for shillings and shillings for pence in each case, and under these conditions the estimated cost was £212 18s. 4d. in excess of the real cost. What was the true cost of the articles?
SQUARES IN STREETS
150. The square of the number of my house is equal to the difference of the squares of the numbers of my next door neighbour’s houses on either side.
My brother, who lives in the next street, can say the same of the number of his house, though his number is not the same as mine. How are our houses numbered?
151.
Two men of unequal strength are set to move a block of marble which weighs 270 lbs., using for the purpose a light plank 6 feet long. The stronger man can carry 180 lbs. How must the block be placed so as to allow him just that share of the weight?
152.
A man has twenty coins, of which some are shillings and the rest half-crowns. If he were to change the half-crowns for sixpences and the shillings for pence he would have 156 coins. How many shillings has he?
COUNT THE COINS
153. Some coins are placed at equal distances apart on a table, so that they form the sides of an equilateral triangle.
From the middle of each side as many are then taken as equal the square root of the number on that side, and placed on the opposite corner coin. The number of coins on each side is then to the original number as 5 is to 4. How many coins are there in all?
PUTTING IN THE POSTS
154. A gardener, wishing to fence round a piece of ground with some light posts, found that if he set them a foot apart there would be 150 too few, but if placed a yard apart there would be 70 to spare. How many posts had he?
155.
A gives B £100 to buy 100 animals, which must be cows at £5 each, sheep at £1, and geese at 1s. How many of each sort can he buy?
156.
John is twice as old as Mary was when he was as old as Mary is. John is now twenty-one. How old is Mary?
157.
In a cricket match A made 35 runs; C and D made respectively half and one-third as many as B, and B’s score was as much below A’s as C’s was above D’s. What did B, C, and D each score?
SETTLED BY REMAINDERS
158. What is the least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10, leaves respectively as remainders 1, 2, 3, 4, 5, 6, 7, 8, and 9?
TABLE TURNING
159. A square table stands on four legs, which are set at the middle point of its sides. What is the greatest weight that this table can uphold upon one of its corners?
BRIBING THE BOYS
160. Well pleased with the inspector’s report, the rector of a country parish came into his school with 99 new pennies in his pocket, and said that he would give them to the five boys in Standard VII. if they could, within an hour, show him how to divide them so that the first share should exceed the second by 3, be less than the third by 10, be greater than the fourth by 9, and less than the fifth by 16. What was the answer which would satisfy these conditions?
SHEEP-STEALING
161. Some Indian raiders carried off a third of a flock of sheep, and a third of a sheep. Another party took a fourth of what remained, and a fourth of a sheep. Others took a fifth of the rest and three-fifths of a sheep. What was the number of the full flock, if there were then 409 left?
162.
Three boys begin to fill a cistern. A brings a pint at the end of every three minutes, B a quart every five minutes, and C a gallon every seven minutes. If the cistern holds fifty-three gallons, in what time will it be filled, and who will pour in the last contribution?
ESTIMATE OF AGE
163. A man late in the last century said that his age was the square root of the year in which he was born. In what year did he say this?
A DEAL IN CHINA
164. A dealer in Eastern curios sold a Satzuma vase for £119, and on calculation found that the number which expressed his profit per cent. expressed also the cost price in pounds of the vase. What was this number?
165.
What is the chance of throwing at least one ace in a single throw with a pair of dice?
166.
A thief starts running from a country house as fast as he can. Four minutes later a policeman starts in pursuit. If both run straight along the road, and the policeman gets over the ground one-third faster than the thief, how soon will he catch him?
167.
Twenty-seven articles are exposed for sale on one of the stalls of a bazaar. What choice has a purchaser?
VERY PERSONAL
168. “How old are you, dad?” said Nellie on her birthday, as her father gave her as many shillings as she was years old. His answer was quite a puzzle for a time, but with the help of her schoolfellows Nellie worked it out.
This is what he said:—
“I was twice as old as you are
The day that you were born.
You will be just what I was then
When fourteen years are gone.”
How old was Nellie, and how old was her dad?