Kingly Kings
Logic
Level
3
How many ways are there to place one white king and one black king on an empty chessboard such that they do not attack each other?
The answer is 3612.
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1 solution
If the first king is placed in a corner, 4 spots around and including it have been removed for the second king to go, so 60 remain. There are 4 corners, so 240 ways using a corner.
If the first king is placed on an edge, 6 spots around and including it have been removed for the second king to go, so 58 remain. There are 24 edge spots, so 1392 ways using an edge.
Finally, if the first king is placed in the middle 6×6 squares, 9 spots around and including it have been removed for the second king to go, so 55 remain. There are 36 edge spots, so 1980 ways to go.
Adding up all the ways, 240+1392+1980 gives 3612 ways.