MAZES AND HOW TO THREAD THEM. 127THE PARADOX PARTY. 137
UNCLASSIFIED PROBLEMS. 142
SOLUTIONS. 148
INDEX. 253
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AMUSEMENTS IN MATHEMATICS. ARITHMETICAL AND ALGEBRAICAL PROBLEMS.
"And what was he?
Forsooth, a great arithmetician." Othello, I. i.
The puzzles in this department are roughly thrown together in classes for the convenience of the reader. Some are very easy, others
quite difficult. But they are not arranged in any order of difficulty--and this is intentional, for it is well that the solver should not be warned that a puzzle is just what it seems to be. It may, therefore, prove to be quite as simple as it looks, or it may contain some pitfall into which, through want of care or over-confidence, we may stumble.
Also, the arithmetical and algebraical puzzles are not separated in the manner adopted by some authors, who arbitrarily require certain problems to be solved by one method or the other. The reader is left to make his own choice and determine which puzzles are capable of being solved by him on purely arithmetical lines.
MONEY PUZZLES.
"Put not your trust in money, but put your money in trust." OLIVER WENDELL HOLMES.
1.--A POST-OFFICE PERPLEXITY.
In every business of life we are occasionally perplexed by some chance question that for the moment staggers us. I quite pitied a young lady in a branch post-office when a gentleman entered and deposited a crown on the counter with this request: "Please give me some twopenny stamps, six times as many penny stamps, and make up the rest of the money in twopence-halfpenny stamps." For a moment she seemed bewildered, then her brain cleared, and with a smile she handed over stamps in exact fulfilment of the order. How long would it have taken you to think it out?
2.--YOUTHFUL PRECOCITY.
The precocity of some youths is surprising. One is disposed to say on occasion, "That boy of yours is a genius, and he is certain to do great things when he grows up;" but past experience has taught us that he invariably becomes quite an ordinary citizen. It is so often the case, on the contrary, that the dull boy becomes a great man. You never can tell. Nature loves to present to us these queer paradoxes. It is well known that those wonderful "lightning calculators," who now and again surprise the world by their feats, lose all their mysterious powers directly they are taught the elementary rules of arithmetic.
A boy who was demolishing a choice banana was approached by a young friend, who, regarding him with envious eyes, asked,
"How much did you pay for that banana, Fred?" The prompt answer was quite remarkable in its way: "The man what I bought it of
receives just half as many sixpences for sixteen dozen dozen bananas as he gives bananas for a fiver."
Now, how long will it take the reader to say correctly just how much Fred paid for his rare and refreshing fruit?
3.--AT A CATTLE MARKET.
Three countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got." "If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I." "Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, Pg 2and then you'll have six times as many animals as I've got here."
No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals
Jakes, Hodge, and Durrant must have taken to the cattle market.
4.--THE BEANFEAST PUZZLE.
A number of men went out together on a bean-feast. There were four parties invited--namely, 25 cobblers, 20 tailors, 18 hatters, and
12 glovers. They spent altogether PS6, 13s. It was found that five cobblers spent as much as four tailors; that twelve tailors spent as
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much as nine hatters; and that six hatters spent as much as eight glovers. The puzzle is to find out how much each of the four parties
spent.
5.--A QUEER COINCIDENCE.
Seven men, whose names were Adams, Baker, Carter, Dobson, Edwards, Francis, and Gudgeon, were recently engaged in play.
The name of the particular game is of no consequence. They had agreed that whenever a player won a game he should double the money of each of the other players--that is, he was to give the players just as much money as they had already in their pockets. They played seven games, and, strange to say, each won a game in turn, in the order in which their names are given. But a more curious coincidence is this--that when they had finished play each of the seven men had exactly the same amount--two shillings and eightpence--in his pocket. The puzzle is to find out how much money each man had with him before he sat down to play.
6.--A CHARITABLE BEQUEST.
A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish; but they were only to continue the gift so long as they could make it in different ways, always giving eighteenpence each to a number of women and half a crown each to men. During how many years could the charity be administered? Of course, by "different ways" is meant a different number of men and women every time.
7.--THE WIDOW'S LEGACY.
A gentleman who recently died left the sum of PS8,000 to be divided among his widow, five sons, and four daughters. He directed that every son should receive three times as much as a daughter, and that every daughter should have twice as much as their mother. What was the widow's share?
8.--INDISCRIMINATE CHARITY.
A charitable gentleman, on his way home one night, was appealed to by three needy persons in succession for assistance. To the first person he gave one penny more than half the money he had in his pocket; to the second person he gave twopence more than half the money he then had in his pocket; and to the third person he handed over threepence more than half of what he had left. On entering his house he had only one penny in his pocket. Now, can you say exactly how much money that gentleman had on him when he started for home?
9.--THE TWO AEROPLANES.
A man recently bought two aeroplanes, but afterwards found that they would not answer the purpose for which he wanted them. So he sold them for PS600 each, making a loss of 20 per cent, on one machine and a profit of 20 per cent, on the other. Did he make a profit on the whole transaction, or a loss? And how much?
10.--BUYING PRESENTS.
"Whom do you think I met in town last week, Brother William?" said Uncle Benjamin. "That old skinflint Jorkins. His family had been taking him around buying Christmas presents. He said to me, 'Why cannot the government abolish Christmas, and make the giving of presents punishable by law? I came out this morning with a certain amount of money in my pocket, and I find I have spent just half of it. In fact, if
