Let \(n \geq 2\) be an integer. An \(n \times n\) board is initially empty. Each minute, you may perform one of three moves:
- If there is an L-shaped tromino region of three cells without stones on the board (rotations not allowed), you may place a stone in each of those cells.
- If all cells in a column have a stone, you may remove all stones from that column.
- If all cells in a row have a stone, you may remove all stones from that row.
For which \(n\) is it possible that, after some nonzero number of moves, the board has no stones?
To perform an action, hover over a collection of cells.