All the numbers to be zero after finitely many operations
Source: IMO Shortlist 1989, Problem 19, ILL 64
September 18, 2008
combinatoricsinvariantChessboardalgorithmIMO Shortlist
Problem Statement
A natural number is written in each square of an chess board. The allowed move is to add an integer to each of two adjacent numbers in such a way that non-negative numbers are obtained. (Two squares are adjacent if they have a common side.) Find a necessary and sufficient condition for it to be possible for all the numbers to be zero after finitely many operations.