Question 30
A 3 × 3 grid has black and white squares. A pattern is balanced if every 2 × 2 subgrid contains exactly two squares of each colour, as in the first example. The second example is unbalanced because its bottom-right 2 × 2 subgrid contains three white squares. Counting rotations and reflections as different, how many balanced 3 × 3 patterns are there?
