Question 67
Let $n\ge 2$ be an integer. Place $n$ rooks on an $n\times n$ chessboard so that no two attack one another. All the rooks move simultaneously, exactly once, and each rook may move only to a square adjacent to its current square.
Determine all values of $n$ for which an initial placement exists such that, after the move, no two rooks still attack one another.
Note: Two squares are adjacent if they share a side.
Determine all values of $n$ for which an initial placement exists such that, after the move, no two rooks still attack one another.
Note: Two squares are adjacent if they share a side.