The non-attacking bishops problem
by John from John D. Cook on (#6X6J0)
How many bishops can you place on a chessboard so that no bishop is attacking any other bishop?
For a standard 8 * 8 chessboard the answer is 14. In general, for an n * n chessboard the answer is 2n - 2.
Here's one way to place the maximum number of non-attacking bishops.
To see that the bishops cannot attack each other, I think it's helpful to imagine extending the chessboard so that each bishop attacks the same number of squares. Then we can see that they miss each other.
