Chess kings
Task number: 3447
How many ways are there to place a black king and a white king on a chessboard such that they do not threaten each other (i.e. they are not on adjacent squares)?
Solution
If the white king is in a corner, the black king has 60 possibilities. If the white king is on the edge of the board, there are 58 possibilities. In other cases there are 55.
Answer
The number of possible positions is \(4{\cdot} 60 + 24{\cdot} 58 +36{\cdot} 55=3{,}612\).
