Chess/Puzzles/Placement/14 Bishops/Solution

There are several solutions to this puzzle, but they are all quite similar. Here's a possible one: 8 bl bl bl bl bl bl 7 6 5 4 3 2 1 bl bl bl bl bl bl bl bl 40 Proof of maximality There are 15 diagonals on the chessboard running from bottom left to top right. They are: a8-a8 a7-b8 a6-c8 a5-d8 a4-e8 a3-f8 a2-g8 a1-h8 b1-h7 c1-h6 d1-h5 e1-h4 f1-h3 g1-h2 h1-h1 Each of these diagonals can only contain one bishop. Also, the first and last diagonals cannot both contain a bishop, since both are on the diagonal a8-h1. Therefore, we can place at most 13 bishops on the other 13 diagonals, and one bishop on those two diagonals, for a total of 14 bishops. Since 14 bishops is possible, 14 is the maximum number of bishops we can place so no two attack each other.