Let $N$ be the number of ways to colour each cell in a $2 \times 50$ rectangle either red or blue such that each $2 \times 2$ block contains at least one blue cell. Show that $N$ is a multiple of $3^{25}$, but not a multiple of $3^{26}$
Problem
Source: New Zealand NZMOC Camp Selection Problems 2018 p7
Tags: Coloring, combinatorial geometry, combinatorics