On an infinite chessboard, a solitaire game is played as follows: at the start, we have
![n^2](/media/m/3/6/a/36a0dd5a7e7ff0e6bbc714e33ddb1d63.png)
pieces occupying a square of side
![n.](/media/m/4/7/8/478d25bfe04800537ae6e85be9d11ea2.png)
The only allowed move is to jump over an occupied square to an unoccupied one, and the piece which has been jumped over is removed. For which
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
can the game end with only one piece remaining on the board?
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On an infinite chessboard, a solitaire game is played as follows: at the start, we have $n^2$ pieces occupying a square of side $n.$ The only allowed move is to jump over an occupied square to an unoccupied one, and the piece which has been jumped over is removed. For which $n$ can the game end with only one piece remaining on the board?