The problem of how to cover a chessboard with the smallest
number of 2-color bishops is presented in a forthcoming article in the
Journal of Recreational Mathematics.
Solutions are shown in the article for all square boards, and
rectangular boards of sizes 2xN, 3xN, 4xN and 5xN.
Unfortunately, the solutions for these boards are too large
to be legible in the journal.
However, webpages can hold enough text to make the 6xN, 7xN and 8xN
solutions legible. (If the lines are too wide in your browser, you can select
a smaller type size.) The following links can be used to see these solutions.