How many ways are there to paint an $m \times n$ board, so that each square is painted blue, white, brown or gold, and in each $2 \times 2$ square there is one square of each color?
Source: Portugal OPM 2018 p3
Tags: Coloring, combinatorics, combinatorial geometry
How many ways are there to paint an $m \times n$ board, so that each square is painted blue, white, brown or gold, and in each $2 \times 2$ square there is one square of each color?