Question 5
(FIN 3; IMO 3) On an infinite chessboard, a solitaire game is played as follows: At the start, we have $n^2$ pieces occupying $n^2$ squares that form a square of side $n$. The only allowed move is a jump horizontally or vertically over an occupied square to an unoccupied one, and the piece that has been jumped over is removed. For what positive integers $n$ can the game end with only one piece remaining on the board?