Roomy Rooks
Logic
Level
3
How many ways are there to place one white rook and one black rook on an empty chessboard such that they do not attack each other?
The answer is 3136.
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1 solution
Without loss of generality. Let's start with the white rook. There are 64 squares to choose from. Once placed, we are left with 49 squares for the black rook to be placed where the two rooks cannot attack each other, regardless of which square we placed the white rook on. Thus, we have
64x49=3136.