Problem

Source: Cono Sur 1992-problem 6

Tags: combinatorics unsolved, combinatorics



Consider a mn board. On each box there's a non-negative integrer number assigned. An operation consists on choosing any two boxes with 1 side in common, and add to this 2 numbers the same integrer number (it can be negative), so that both results are non-negatives. What conditions must be satisfied initially on the assignment of the boxes, in order to have, after some operations, the number 0 on every box?.