Question

How many ways are there to place two identical kings on an 8×8 chessboard so that the kings are not in adjacent squares? on an n ×m chessboard?

Answer 1

Thank you for asking this question.

Here is your answer:

The first King could be on a corner square(4 ways), leaving 60 other squares for the next King.

The first King could be on a edge square(24 ways), leaving 58 other squares for the next King.

The first King could be on a central square(36 ways), leaving 55 other squares for the next King.

This will double count the configurations, so we have (4×60+24×58+36×55)/2=1806.

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