5

Part of 2024 International Zhautykov Olympiad

Problems(1)

Dominoes and 3x1 stripes

Source: IZhO 2024, P5

m\times n

table tiled with

3\times 1

stripes and we are given that

6 | mn

. Prove that there exists a tiling of the table with

2\times 1

dominoes such that each of these stripes contains one whole domino.