March of the Rooks
Probability
Level
1
How many ways are present to put one white and one black rook on a chessboard so that they do not attack each other?
Image Credit: Wikimedia Alan Light
The answer is 3136.
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1 solution
The white
whenever placed at any of the squares of the chessboard attacks exactly 14 squares + 1 square (on which it is placed). This leaves 64-15 = 49 squares for the other black
to be placed without danger.
Therefore there are 6 4 × 4 9 ways where the two rooks can be placed without any of the two attacking each other:
3 1 3 6