Download e-book for kindle: Hexaflexagons, Probability Paradoxes, and the Tower of by Martin Gardner

By Martin Gardner

ISBN-10: 0521756154

ISBN-13: 9780521756150

Hexaflexagons, likelihood Paradoxes, and the Tower of Hanoi is the inaugural quantity within the New Martin Gardner Mathematical Library sequence. dependent off of Gardener's tremendously renowned medical American columns, his puzzles and demanding situations can now fascinate a complete new iteration! Paradoxes and paper-folding, Moebius diversifications and mnemonics, fallacies, magic sq., topological curiosities, parlor methods, and video games historical and glossy, from Polyminoes, Nim, Hex, and the Tower of Hanoi to 4-dimensional ticktacktoe. those mathematical recreations, essentially and cleverly awarded via Martin Gardner, pride and perplex whereas demonstrating ideas of common sense, likelihood, geometry, and different fields of arithmetic. Now the writer, in session with specialists, has extra updates to the entire chapters, together with new video game adaptations, mathematical proofs, and different advancements and discoveries.

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Extra info for Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games

Example text

More likely than not, at least two dates will match, often much to the astonishment of the parties concerned who may have known each other for years. Fortunately, it does not matter in the least if anyone cheats by giving an incorrect date. The odds remain exactly the same. An even easier way to test the paradox is by checking birth dates on 24 names picked at random from a Who’s Who or some other biographical dictionary. Of course the more names you check beyond 24, the greater the probability of a coincidence.

This square seems to have no system: The numbers appear to be distributed in the matrix at random. Nevertheless, the square possesses a magical property as astonishing to most mathematicians as it is to laymen. A convenient way to demonstrate this property is to equip yourself with five pennies and 20 little paper markers (say pieces of paper matches). Now ask someone to pick any number in the square. Lay a penny on this number and eliminate all the other numbers in the same row and in the same column by covering them with markers.

AFTERWORD, 1988 In the chapter on ticktacktoe, I said that the three-dimensional 4 × 4 × 4 game was unsolved. Oren Patashnik, at Bell Laboratories, Ticktacktoe 45 cracked the game in 1977 with a computer program almost as complex as the program that proved the four-color map conjecture in 1976. Details are given in Patashnik’s article, cited in the bibliography. Incidentally, the proof that the first player can always win a game of Hex if he plays correctly (Chapter 8) also applies to ticktacktoe games.

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Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games by Martin Gardner

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