536 Puzzles and Curious Problems (Dover Math Games & Puzzles) - Softcover

Dudeney, Henry E.

Softcover

ISBN 10: 0486796868 ISBN 13: 9780486796864

Publisher: Dover Publications, 2016

Synopsis

For two decades, self-taught mathematician Henry E. Dudeney wrote a puzzle page, "Perplexities," for The Strand Magazine. Martin Gardner, longtime editor of Scientific American's mathematical games column, hailed Dudeney as "England's greatest maker of puzzles," unsurpassed in the quantity and quality of his inventions. This compilation of Dudeney's long-inaccessible challenges attests to the puzzle-maker's gift for creating witty and compelling conundrums.
This treasury of intriguing puzzles begins with a selection of arithmetical and algebraical problems, including challenges involving money, time, speed, and distance. Geometrical problems follow, along with combinatorial and topological problems that feature magic squares and stars, route and network puzzles, and map coloring puzzles. The collection concludes with a series of game, domino, match, and unclassified puzzles. Solutions for all 536 problems are included, and charming drawings enliven the book.

About this title

About the Author

English author and mathematician Henry E. Dudeney (1857–1930) specialized in logic and mathematical puzzles. His column, "Perplexities," was a regular feature in The Strand Magazine for 20 years, and in 1926 he published the first known crossnumber puzzle.

From the Back Cover

For two decades, self-taught mathematician Henry E. Dudeney wrote a puzzle page, "Perplexities," for The Strand Magazine. Martin Gardner, longtime editor of Scientific American's mathematical games column, hailed Dudeney as "England's greatest maker of puzzles," unsurpassed in the quantity and quality of his inventions. This compilation of Dudeney's long-inaccessible challenges attests to the puzzle-maker's gift for creating witty and compelling conundrums.
This treasury of intriguing puzzles begins with a selection of arithmetical and algebraical problems, including challenges involving money, time, speed, and distance. Geometrical problems follow, along with combinatorial and topological problems that feature magic squares and stars, route and network puzzles, and map coloring puzzles. The collection concludes with a series of game, domino, match, and unclassified puzzles. Solutions for all 536 problems are included, and charming drawings enliven the book.
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Excerpt. © Reprinted by permission. All rights reserved.

536 Puzzles and Curious Problems

By Henry Ernest Dudeney, Martin Gardner

Dover Publications, Inc.

Copyright © 2016 Henry Ernest Dudeney
All rights reserved.

ISBN: 978-0-486-79686-4

Contents

INTRODUCTION, 
ARITHMETICAL AND ALGEBRAICAL PROBLEMS, 
Money Puzzles, 
Age Puzzles, 
Clock Puzzles, 
Speed and Distance Puzzles, 
Weight Puzzles, 
Digital Puzzles, 
Skeleton Puzzles, 
Cryptarithm Puzzles, 
Miscellaneous Puzzles, 
GEOMETRICAL PROBLEMS, 
Triangle, Square, and other Polygon Puzzles, 
Circle Puzzles, 
Dividing-the-Plane Puzzles, 
Plane Geometry Puzzles, 
Solid Geometry Puzzles, 
Dissection Puzzles, 
Paper Folding Puzzles, 
Moving Counter Puzzles, 
COMBINATORIAL AND TOPOLOGICAL PROBLEMS, 
Magic Square Puzzles, 
Magic Star Puzzles, 
Liquid Pouring Puzzles, 
Route and Network Puzzles, 
Point Alignment Puzzles, 
Map Coloring Puzzles, 
Miscellaneous Combinatorial Puzzles, 
GAME PUZZLES, 
DOMINO PUZZLES, 
MATCH PUZZLES, 
UNCLASSIFIED PUZZLES, 
ANSWERS, 
INDEX, 

CHAPTER 1

Arithmetic & Algebraic Problems

Arithmetic & Algebraic Problems

1. CONCERNING A CHECK

A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

2. DOLLARS AND CENTS

A man entered a store and spent one-half of the money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as he had cents when he went in. How much money did he have on him when he entered?

3. LOOSE CASH

What is the largest sum of money — all in current coins and no silver dollars — that I could have in my pocket without being able to give change for a dollar, half dollar, quarter, dime, or nickel?

4. GENEROUS GIFTS

A generous man set aside a certain sum of money for equal distribution weekly to the needy of his acquaintance. One day he remarked, "If there are five fewer applicants next week, you will each receive two dollars more." Unfortunately, instead of there being fewer there were actually four more persons applying for the gift.

"This means," he pointed out, "that you will each receive one dollar less."

How much did each person receive at that last distribution?

5. BUYING BUNS

Buns were being sold at three prices: one for a penny, two for a penny, and three for a penny. Some children (there were as many boys as girls) were given seven pennies to spend on these buns, each child to receive exactly the same value in buns. Assuming that all buns remained whole, how many buns, and of what types, did each child receive?

6. UNREWARDED LABOR

A man persuaded Weary Willie, with some difficulty, to try to work on a job for thirty days at eight dollars a day, on the condition that he would forfeit ten dollars a day for every day that he idled. At the end of the month neither owed the other anything, which entirely convinced Willie of the folly of labor. Can you tell just how many days' work he put in and on how many days he idled?

7. THE PERPLEXED BANKER

A man went into a bank with a thousand dollars, all in dollar bills, and ten bags. He said, "Place this money, please, in the bags in such a way that if I call and ask for a certain number of dollars you can hand me over one or more bags, giving me the exact amount called for without opening any of the bags."

How was it to be done? We are, of course, only concerned with a single application, but he may ask for any exact number of dollars from one to one thousand.

8. A WEIRD GAME

Seven men engaged in play. Whenever a player won a game he doubled the money of each of the other players. That is, he gave each player just as much money as each had in his pocket. They played seven games and, strange to say, each won a game in turn in the order of their names, which began with the letters A, B, C, D, E, F, and G.

When they had finished it was found that each man had exactly $1.28 in his pocket. How much had each man in his pocket before play?

9. DIGGING A DITCH

Here is a curious question that is more perplexing than it looks at first sight. Abraham, an infirm old man, undertook to dig a ditch for two dollars. He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities. Abraham could dig as fast as Benjamin could shovel out the dirt, and Benjamin could dig four times as fast as Abraham could do the shoveling.

How should they divide the money? Of course, we must assume their relative abilities for work to be the same in digging or shoveling.

10. NAME THEIR WIVES

A man left a legacy of $ 1,000.00 to three relatives and their wives. The wives received together $396.00. Jane received $10.00 more than Catherine, and Mary received $10.00 more than Jane. John Smith was given just as much as his wife, Henry Snooks got half as much again as his wife, and Tom Crowe received twice as much as his wife. What was the Christian name of each man's wife?

11. MARKET TRANSACTIONS

A farmer goes to market and buys a hundred animals at a total cost of $1,000.00. The price of cows being $50.00 each, sheep $10.00 each, and rabbits 50¢ each, how many of each kind does he buy? Most people will solve this, if they succeed at all, by more or less laborious trial, but there are several direct ways of getting the solution.

12. THE SEVEN APPLEWOMEN

Here is an old puzzle that people are frequently writing to me about. Seven applewomen, possessing respectively 20, 40, 60, 80, 100, 120, and 140 apples, went to market and sold all their apples at the same price, and each received the same sum of money. What was the price?

13. A LEGACY PUZZLE

A man left legacies to his three sons and to a hospital, amounting in all to $1,320.00. If he had left the hospital legacy also to his first son, that son would have received as much as the other two sons together. If he had left it to his second son, he would have received twice as much as the other two sons together. If he had left the hospital legacy to his third son, he would have received then thrice as much as the first son and second son together. Find the amount of each legacy.

14. PUZZLING LEGACIES

A man bequeathed a sum of money, a little less than $1,500.00, to be divided as follows: The five children and the lawyer received such sums that the square root of the eldest son's share, the second son's share divided by two, the third son's share minus $2.00, the fourth son's share plus $2.00, the daughter's share multiplied by two, and the square of the lawyer's fee all worked out at exactly the same sum of money. No dollars were divided, and no money was left over after the division. What was the total amount bequeathed?

15. DIVIDING THE LEGACY

A man left $100.00 to be divided between his two sons Alfred and Benjamin. If one-third of Alfred's legacy be taken from one-fourth of Benjamin's, the remainder would be $11.00. What was the amount of each legacy?

16. A NEW PARTNER

Two partners named Smugg and Williamson have decided to take a Mr. Rogers into partnership. Smugg has 1½ times as much capital invested in the business as Williamson, and Rogers has to pay down $2,500.00, which sum shall be divided between Smugg and Williamson, so that the three partners shall have an equal interest in the business. How shall the sum be divided?

17. POCKET MONEY

"When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a newspaper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?"

18. DISTRIBUTION

Nine persons in a party, A, B, C, D, E, F, G, H, K, did as follows: First A gave each of the others as much money as he (the receiver) already held; then B did the same; then C; and so on to the last, K giving to each of the other eight persons the amount the receiver then held. Then it was found that each of the nine persons held the same amount.

Can you find the smallest amount in cents that each person could have originally held?

19. REDUCTIONS IN PRICE

"I have often been mystified," said Colonel Crackham, "at the startling reductions some people make in their prices, and wondered on what principle they went to work. For example, a man offered me a motorcycle two years ago for $1,024.00; a year later his price was $640.00; a little while after he asked a level $400.00; and last week he was willing to sell for $250.00. The next time he reduces I shall buy. At what price shall I purchase if he makes a consistent reduction?"

20. HORSES AND BULLOCKS

A dealer bought a number of horses at $344.00 each, and a number of bullocks at $265.00 each. He then discovered that the horses had cost him in all $33.00 more than the bullocks. Now, what is the smallest number of each that he must have bought?

21. BUYING TURKEYS

A man bought a number of turkeys at a cost of $60.00, and after reserving fifteen of the birds he sold the remainder for $54.00, thus gaining 10¢ a head by these. How many turkeys did he buy?

22. THE THRIFTY GROCER

A grocer in a small business had managed to put aside (apart from his legitimate profits) a little sum in dollar bills, half dollars, and quarters, which he kept in eight bags, there being the same number of dollar bills and of each kind of coin in every bag. One night he decided to put the money into only seven bags, again with the same number of each kind of currency in every bag. And the following night he further reduced the number of bags to six, again putting the same number of each kind of currency in every bag.

The next night the poor demented miser tried to do the same with five bags, but after hours of trial he utterly failed, had a fit, and died, greatly respected by his neighbors. What is the smallest possible amount of money he had put aside?

23. THE MISSING PENNY

Here is an ancient puzzle that has always perplexed some people. Two market women were selling their apples, one at three for a penny and the other at two for a penny. One day they were both called away when each had thirty apples unsold: these they handed to a friend to sell at five for 2¢. It will be seen that if they had sold their apples separately they would have fetched 25¢, but when they were sold together they fetched only 24¢.

"Now," people ask, "what in the world has become of that missing penny?" because, it is said, three for 1¢ and two for 1¢ is surely exactly the same as five for 2¢.

Can you explain the little mystery?

24. THE RED DEATH LEAGUE

The police, when making a raid on the headquarters of a secret society, secured a scrap of paper similar to the one pictured.

"That piece of paper," said the detective, throwing it on the table, "has worried me for two or three days. You see it gives the total of the subscriptions for the present year as $3,007.37, but the number of members (I know it is under 500) and the amount of the subscription have been obliterated. How many members were there in the Red Death League, and what was the uniform subscription?"

Of course, no fraction of a cent is permitted.

25. A POULTRY POSER

Three chickens and one duck sold for as much as two geese; one chicken, two ducks, and three geese were sold together for $25.00. What was the price of each bird in an exact number of dollars?

26. BOYS AND GIRLS

Nine boys and three girls agreed to share equally their pocket money. Every boy gave an equal sum to every girl, and every girl gave another equal sum to every boy. Every child then possessed exactly the same amount. What was the smallest possible amount that each then possessed?

27. THE COST OF A SUIT

"Hello, old chap," cried Russell as Henry Melville came into the club arrayed in a startling new tweed suit, "have you been successful in the card-room lately? No? Then why these fine feathers?"

"Oh, I just dropped into my tailor's the other day," he explained, "and this cloth took my fancy. Here is a little puzzle for you. The coat cost as much as the trousers and vest. The coat and two pairs of trousers would cost $175.00. The trousers and two vests would cost $100.00. Can you tell me the cost of the suit?"

28. A QUEER SETTLING UP

Professor Rackbrane told his family at the breakfast table that he had heard the following conversation in a railway carriage the night before.

One passenger said to another, "Here is my purse: give me just as much money, Richard, as you find in it."

Richard counted the money, added an equal value from his own pocket, and replied, "Now, John, if you give me as much as I have left of my own we shall be square."

John did so, and then stated that his own purse contained $3.50, while Richard said that he now had $3.00. How much did each man possess at first?

29. APPLE TRANSACTIONS

A man was asked what price per 100 he paid for some apples, and his reply was as follows: "If they had been 4¢ more per 100 I should have got five less for $1.20." Can you say what was the price per 100?

30. PROSPEROUS BUSINESS

A man started business with a capital of $2,000.00, and increased his wealth by 50 per cent every three years. How much did he possess at the expiration of eighteen years?

31. THE BANKER AND THE COUNTERFEIT BILL

A banker in a country town was walking down the street when he saw a five-dollar bill on the curb. He picked it up, noted the number, and went to his home for luncheon. His wife said that the butcher had sent in his bill for five dollars, and, as the only money he had was the bill he had found, he gave it to her, and she paid the butcher. The butcher paid it to a farmer in buying a calf, the farmer paid it to a merchant who in turn paid it to a laundry woman, and she, remembering that she owed the bank five dollars, went there and paid the debt.

The banker recognized the bill as the one he had found, and by that time it had paid twenty-five dollars worth of debts. On careful examination he discovered that the bill was counterfeit. What was lost in the whole transaction, and by whom?

32. THEIR AGES

If you add the square of Tom's age to the age of Mary, the sum is 62; but if you add the square of Mary's age to the age of Tom, the result is 176. Can you say what are the ages of Tom and Mary?

33. MRS. WILSON'S FAMILY

Mrs. Wilson had three children: Edgar, James, and John. Their combined ages were half of hers. Five years later, during which time Ethel was born, Mrs. Wilson's age equalled the total of all her children's ages. Ten years more have now passed, Daisy appearing during that interval. At the latter event Edgar was as old as John and Ethel together. The combined ages of all the children are now double Mrs. Wilson's age, which is, in fact, only equal to that of Edgar and James together. Edgar's age also equals that of the two daughters.

Can you find all their ages?

34. DE MORGAN AND ANOTHER

Augustus De Morgan, the mathematician, who died in 1871, used to boast that he was x years old in the year x. Jasper Jenkins, wishing to improve on this, told me in 1925 that he was a2 + b2 in a4 + b4; that he was 2m in the year 2m2; and that he was 3n4 years old in the year 3n. Can you give the years in which De Morgan and Jenkins were respectively born?

35. "SIMPLE" ARITHMETIC

When visiting an insane asylum, I asked two inmates to give me their ages. They did so, and then, to test their arithmetical powers, I asked them to add the two ages together. One gave me 44 as the answer, and the other gave 1,280.1 immediately saw that the first had subtracted one age from the other, while the second person had multiplied them together. What were their ages?

36. ANCIENT PROBLEM

Here is an example of the sort of "Breakfast Problem" propounded by Metrodorus in 310 A.D.

Demochares has lived one-fourth of his life as a boy, one-fifth as a youth, one-third as a man, and has spent thirteen years in his dotage. How old is the gentleman?

37. FAMILY AGES

A man and his wife had three children, John, Ben, and Mary, and the difference between their parents' ages was the same as between John and Ben and between Ben and Mary. The ages of John and Ben, multiplied together, equalled the age of the father, and the ages of Ben and Mary multiplied together equalled the age of the mother. The combined ages of the family amounted to ninety years. What was the age of each person?

38. MIKE'S AGE

"Pat O'Connor," said Colonel Crackham, "is now just one and one-third times as old as he was when he built the pig sty under his drawing-room window. Little Mike, who was forty months old when Pat built the sty, is now two years more than half as old as Pat's wife, Biddy, was when Pat built the sty, so that when little Mike is as old as Pat was when he built the sty, their three ages combined will amount to just one hundred years. How old is little Mike?"

39. THEIR AGES

Rackbrane said the other morning that a man on being asked the ages of his two sons stated that eighteen more than the sum of their ages is double the age of the elder, and six less than the difference of their ages is the age of the younger. What are their ages?

40. BROTHER AND SISTER

A boy on being asked the age of himself and of his sister replied:

"Three years ago I was seven times as old as my sister; two years ago I was four times as old; last year I was three times as old; and this year I am two and one-half times as old."

(Continues...)

Excerpted from 536 Puzzles and Curious Problems by Henry Ernest Dudeney, Martin Gardner. Copyright © 2016 Henry Ernest Dudeney. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Edition details

• Publisher: Dover Publications
• Publication date: 2016
• Language: English
• ISBN 10: 0486796868
• ISBN 13: 9780486796864
• Binding: Paperback
• Edition number: 1
• Number of pages: 448
• Editor: Gardner Martin