n.t.tuan
26-02-2008, 04:01 PM
We have a board n on n. In every square we have an integer. The sum of all integers on the board is 0. We define an action on a square. Due to the action the integer on the square is deacreased by the number of neighbouring squares, and the number inside every of the neighbouring squares is increased by 1. Determine if there exists n\geq 2 such that we can turn all the integers into zeros in a finite number of actions.