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1993 IMO Problems/Problem 3

Revision as of 14:34, 6 October 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem == On an infinite chessboard, a game is played as follows. At the start, <math>n^2</math> pieces are arranged on the chessboard in an <math>n</math> by <math>n</math...")
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Problem

On an infinite chessboard, a game is played as follows. At the start, $n^2$ pieces are arranged on the chessboard in an $n$ by $n$ block of adjoining squares, one piece in each square. A move in the game is a jump in a horizontal or vertical direction over an adjacent occupied square to an unoccupied square immediately beyond. The piece which has been jumped over is removed. Find those values of $n$ for which the game can end with only one piece remaining on the board.

Solution

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