MathDB

Let

n\geq 2

be a positive integer. On an

n\times n

board,

n

rooks are placed in such a manner that no two attack each other. All rooks move at the same time and are only allowed to move in a square adjacent to the one in which they are located. Determine all the values of

n

for which there is a placement of the rooks so that, after a move, the rooks still do not attack each other.
Note: Two squares are adjacent if they share a common side.

Problem Statement