By Martin Gardner

ISBN-10: 0226282546

ISBN-13: 9780226282541

Those in actual fact and cleverly awarded mathematical recreations of paradoxes and paperfolding, Moebius diversifications and mnemonics either historical and glossy satisfaction and perplex whereas demonstating ideas of common sense, likelihood, geometry, and different mathematical fields.
"A classic."--Andrew Rothery, Times schooling Supplement
"Martin Gardner has became a trick as neat as any within the ebook itself. He has chosen a gaggle of diversions which aren't in basic terms interesting yet mathematically significant in addition. the result's a piece that is worthwhile on nearly each point of mathematical achievement."--Miriam Hecht, Iscripta Mathematica

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Additional info for Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games

Example text

Unfortunately, the robot can spring its own t r a p by following with cell 9, then 5 on its next move. It might turn out that in actual play the machine would win more often by this reckless strategy than with a safe course that would most likely end in a draw. A truly master player, robot or human, would not only know the most probable responses of novices, a s determined by statistical studies of past games; he would also analyze each opponent's style of play to determine what sort of mistakes the opponent would most likely make.

With this restriction the game is a draw if played rationally, but it swarms with potential traps on both sides. A variation of this game permits moves to neighboring 40 Ticktacktoe cells along the two main diagonals of the square. , a move can be made from cell 2 to cell 4 ) . I n the first version the initial player can still force a win if allowed to open on the center, but the second variant is probably a draw. A free-wheeling version called les pendus (the hanged) in France, permits any piece to be moved to any vacant cell.

I f w e accept the proposed solution, w e m u s t believe that liars can always be made the dupes o f their ozun principles, a situation, indeed, zuhich is bound to arise whenever lying takes the form o f slavish adherence to arbitrary rules. " expecting h i m to interpret the question as counterfactual conditional in meaning as well as f o r m , presupposes a certain preciosity on the part o f the native. " O n the other hand, i f he fixes h i m w i t h a glittering eye in order t o emphasize the logical intent o f the question, he also reveals i t s purpose, arousing the native's suspicion that he i s being tricked.

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Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games by Martin Gardner

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