MathDB

Given a chessboard

n \times n

, where

n\geq 4

and

p=n+1

is a prime number. A set of

n

unit squares is called tactical if after putting down queens on these squares, no two queens are attacking each other. Prove that there exists a partition of the chessboard into

n-2

tactical sets, not containing squares on the main diagonals.
Queens are allowed to move horizontally, vertically and diagonally.

Problem Statement