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2 colours in a 2x8 board (2021 May Olympiad L1 p2)

Source:

August 20, 2021
combinatoricsColoring

Problem Statement

In a 2×82 \times 8 squared board, you want to color each square red or blue in such a way that on each 2×22 \times 2 sub-board there are at least 33 boxes painted blue. In how many ways can this coloring be done?
Note. A 2×22 \times 2 board is a square made up of 44 squares that have a common vertex.