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The most bishops that cannot attack each other

chessboardextremaldiagonalsbishops

A bishop attacks along both of its diagonals.

What is the largest number of bishops that can be placed on an 8 by 8 chessboard so that no two attack each other? Prove the bound and give an arrangement.

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Count the diagonals running in one direction (say from bottom-left to top-right). Two bishops on the same such diagonal attack each other. How many of those diagonals are there, and can all of them be used?

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