Problem

Source: Ukraine 2005 grade 8

Tags: combinatorics proposed, combinatorics



A $ 6 \times 6$ board is filled out with positive integers. Each move consists of selecting a square larger than $ 1 \times 1$, consisting of entire cells, and increasing all numbers inside the selected square by $ 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$?