Martin Gardner continues to delight, by introducing readers to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles.
Table of Contents
1. The Five Platonic Solids
3. Henry Ernest Dudeney: England’s Greatest Puzzlist
4. Digital Roots
5. Nine Problems
6. The Soma Cube
7. Recreational Topology
8. Phi: The Golden Ratio
9. The Monkey and the Coconuts
11. Recreational Logic
12. Magic Squares
13. James Hugh Riley Shows, Inc.
14. Nine More Problems
15. Eleusis: The Induction Game
17. Squaring the Square
18. Mechanical Puzzles
19. Probability and Ambiguity
20. The Mysterious Dr. Matrix
Excerpt: Ch. 9 The Monkey and the Coconut (p. 91)
In the October 9, 1926, issue of The Saturday Evening Post appeared a short story by Ben Ames William entitled "Coconuts." The story concerned a building contractor who was anxious to prevent a competitor from getting an important contract. A shrewd employee of the contracto, knowing the competitor's passion for recreational mathematics, presented him with a problem so exasperating that while he was preoccupied with solving it, he forgot to enter his bid before the deadline.
Here is the problem exactly as the clerk in William's story phrased it:
Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. Piled them all up together and then went to sleep for the night.
But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided the coconuts into five piles. He had one coconut left over, and he gave that to the monkey, and he hid his pile and put the rest all back together.
By and by the next man woke and did the same thing. Ane he had one left over, and he gave it to the monkey. And all five of the men did the same thing,one after the other; each one taking a fifth of the coconuts in the pile when he woke up, and each having one left over for the monkey. And in the morning they divided what cocnuts were left, and they came out in five equal shares. Of course each one must have known there were coconuts missing; but each one was guilty as the others, so they didn't say anything. How many coconuts were there in the beginning?
Williams neglected to include the answer in his story. It is said that the offices of The Saturday Evening Post were showered with some 2,000 letters during the first week after the issue appeared. George Horace Lorimer, then editor-in-chief, sent Williams the following historic wire:
FOR THE LOVE OF MIKE, HOW MANY COCONUTS? HELL POPPING AROUND HERE.
For 20 years, Williams continued to receive letters requesting the answer or proposing new solutions. Today the problem of the coconuts is probably the most worked on and least often solved of all the Diophantine brain-teasers. (The term "Diophantine" is descended from Diophantus of Alexandria, a Greek algebraist who was the first to analyze extensively equations calling for solutions in rational numbers.)
Williams did not invent the coconut problem. He merely altered a much older problem to make it more confusing. The older version is the same except that in the morning, when the final division is made, there is again an extra coconut for the monkey; in William's version the final division comes out even. Some Diophantine equations have only one answer (e.g., x2 + 2 = y3); some have a finite number of answers; some (e.g., x3 + y3 = z3) have no answer. Both William's version of the coconut problem and its predecessor have an infinite number of answers in whole numbers. Our task is to find the smallest positive number.
About the Author
For 25 of his 94 years, Martin Gardner wrote “Mathematical Games and Recreations,” a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of mathematics. He has also made significant contributions to magic, philosophy, children’s literature, and the debunking of pseudoscience. He has produced more than 60 books, including many best sellers, most of which are still in print. His Annotated Alice has sold more than one million copies.