IMO Shortlist 1993 problem G5


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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?
Izvor: Međunarodna matematička olimpijada, shortlist 1993