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.

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