Peaceable Armies of Queens

2021 Problem solving

The problem of the peaceful army of queens is introduced by Robort Bosch in 1999. Consider a chessboard of size n with two equal sets of queens of different colors whose queens of different colors must not be put in check. For which the number of queens must be maximized.

All optimal solutions with symmetries

n	Solutions	Complet
2	1	[ ]
3	16	[ ]
4	112	[x]
5	18	[x]
6	560	[x]
7	304	[x]
8	?	[ ]

• n = 4, count = 112
• n = 5, count = 18
• n = 6, count = 560
• n = 7, count = 304

Refs

• A250000

• coexx.gms : Peacefully Coexisting Armies of Queens - tight

• P110: Peaceably Co-existing Armies of Queens