1993 IMO Problems/Problem 3

Problem

On an infinite chessboard, a game is played as follows. At the start, pieces are arranged on the chessboard in an by 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 for which the game can end with only one piece remaining on the board.

Video Solution

This is a very beautifully done video solution: https://www.youtube.com/watch?v=eAROaUpkgRo Even though he made a mistake when reducing the 5x5 to a 2x2 as someone pointed out in the comments.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1993 IMO (Problems) • Resources
Preceded by Problem 2	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 4
All IMO Problems and Solutions