Chess and Mathematics

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This page, which is currently under construction, will highlight a few ways in which mathematics relates to the realms of chess:

• There is a legend that, when the inventor of chess showed his invention to the king of Persia, the king asked him what he would like as a reward. The inventor said that he "just" wanted one grain of wheat for the first square on the chessboard, two grains of wheat for the second square, four for the third square, and so on, doubling the amount on each square. The king agreed, thinking that to be a small reward for inventing such an interesting game, but before he had calculated the amount required for the first 32 squares of the 64-square chessboard, he changed his mind and had the inventor executed instead. How much grain would he have had to pay the inventor (see the exponential growth page for answer)? This legend illustrates how quickly a quantity can grow exponentially.
• Combinatorics: There are 400 different ways for both sides to play the first move in a game of chess. There are 197,281 ways for both sides to play the first two moves. There are an estimated 318,979,564,000 ways of playing the first four moves. There are about 169,518,829,100,544,000,000,000,000,000 ways of playing the first ten moves.
• Recreational mathematics: See, for example, Eight Queens Puzzle, Knight's Tour, and Knight's Tour Magic Square.

You can view a large number of chess games on allthatstuff.info.