MathDB
board

Source: Ukraine 2005 grade 8

July 24, 2009
combinatorics proposedcombinatorics

Problem Statement

A 6×6 6 \times 6 board is filled out with positive integers. Each move consists of selecting a square larger than 1×1 1 \times 1, consisting of entire cells, and increasing all numbers inside the selected square by 1 1. Is it always possible to perform several moves so as to reach a situation where all numbers on the board are divisible by 3 3?