Problem

Source: Caucasus 2015 8.3

Tags: Tiling, tiles, combinatorics, combinatorial geometry



The workers laid a floor of size $n \times n$ with tiles of two types: $2 \times 2$ and $3 \times 1$. It turned out that they were able to completely lay the floor in such a way that the same number of tiles of each type was used. Under what conditions could this happen? (You can’t cut tiles and also put them on top of each other.)