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T H E S E C O N D S C I E N T I F C C - L M E R I C A N B O O K 0 F MATHEMATICAL PUZZLES AND D I V E R S I O N S 1 M A R T I N G A R D N E R
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THE SECOND SCIENTIFIC AMERICAN BOOK OF Mathematical Puzzles & Diversions
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The 2nd SCIENTIFIC AMERICAN Book of I L L U S T R A T E D W I T H D R A W I N G S A N D D I A G R A M S
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MARTIN GARDNER Mathematical Puzzles A NEW SELECTION : from Origami to Recreational Logic, from Digital Roots and Dudeney Puzzles to the Diabolic Square, from the Golden Ratio to the Generalized Ham Sandwich Theorem. With mathematical commentaries b y Mr. Gardner, ripostes from readers of Scientific American, references for further reading and, of course, solutions. With a new Postscript by the author T H E U N I V E R S I T Y O F C H I C A G O P R E S S
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Material previously published in Scienti,fic American is copyright O 1958,1959,1960 by Scientific American, Inc. Most of the drawings and diagrams appear by courtesy of Scientijic American, in whose pages they were originally published. The University of Chicago Press, Chicago 60637 Copyright O 1961,1987 by Martin Gardner All rights reserved. Published 1961 University of Chicago Press Edition 1987 Printed in the United States of America Library of Congress Cataloging in Publication Data Gardner, Martin, 1914- The 2nd Scientific American book of mathematical puzzles & diversions. Reprint. Originally published as v. 2 of The Scientific American book of mathematical puzzles & diversions. New York : Simon and Schuster, 1961. Bibliography: p. 1. Mathematical recreations. I. Scientific American. 11. Title. 111. Title: Second Scientific American book of mathematical puzzles & diversions. QA95.Gl6 1987 793.7'4 87-10760 ISBN 0-22628253-8 (pbk.)
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For J . H . G. who likes to tackle puzzles big enough to walk upon
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C O N T E N T S INTRODUCTION The Five Platonic Solids [Answers on page 221 Henry Ernest Dudeney: England's Greatest Puxxlist [Answers on page 411 Digital Roots [Answers on page 601 Nine Problems [Answers on page 561 The Soma Cube [Answers on page '771 Recreational Topology [Answers on page 881 Phi: The Golden Ratio [Answers on page 1021 The Monkey and the Coconuts [Answers on page 1101 Recreational Logic [Answers on page 1271 Magic Squares James Hugh Riley Shows, Inc. [Answers on page 1491 Nine More Problems [Answers on page 1561 Eleusis : The Induction Game [Answers on page 1'721
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8 Contents 16. Origami [Answers on page 1841 17. Squaring the Square 186 18. Mechanical Puzzles [Answers on page 2181 19. Probability and Ambiguity [Answers on page 2291 20. The Mysterious Dr. Matrix 233 [Answers on page 2421 REFERENCES FOR FURTHER READING 245 POSTSCRIPT 253
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I N T R O D U C T I O N SINCE THE APPEARANCE of the first Scientific American Book of Mathematical Puzzles & Diversions, in 1959, popular in- terest in recreational mathematics has continued to increase. Many new puzzle books have been printed, old puzzle books reprinted, kits of recreational math materials are on the market, a new topological game (see Chapter 7 ) has caught the fancy of the country's youngsters, and an excellent little magazine called Recreational Mathematics has been started by Joseph Madachy, a research chemist in Idaho Falls. Chess-
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  • Fall '16
  • Statistics, Platonic solid, Platonic solids, HENRY ERNEST DUDENEY

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