Chess/Puzzles/Placement/14 Bishops/Solution

There are several solutions to this puzzle, but they are all quite similar.

Here's a possible one:

a b c d e f g h 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 a b c d e f g h

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.