MathNet 2019-part-07 — 184 problems (EN–VI) Question 119

Let $m$ and $n$ be positive integers, neither is divisible by $6$. A rectangle $m \times n$ is filled with $2 \times 2$ and $3 \times 3$ squares. Show that such rectangle can be filled with squares of one of the types: $2 \times 2$ or $3 \times 3$.

(Edvard Turkevych)



**Fig. 12**