n pieces on the squares of a 5 x 9 board, game to the end of the world
Source: Switzerland - Swiss TST 2003 p5
February 18, 2020
gamecombinatorial geometrycombinatoricsboard
Problem Statement
There are pieces on the squares of a board, at most one on each square at any time during the game. A move in the game consists of simultaneously moving each piece to a neighboring square by side, under the restriction that a piece having been moved horizontally in the previous move must be moved vertically and vice versa. Find the greatest value of for which there exists an initial position starting at which the game can be continued until the end of the world.