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.