A 3 × 3 grid has a pattern of black and white squares. A pattern is called balanced if each 2 × 2 subgrid contains exactly two squares of each colour, as seen in the first example. The pattern in the second example is unbalanced because the balanced bottom-right 2 × 2 subgrid contains three white squares. Counting rotations and reflections as different, how many bal- anced 3 × 3 patterns are there?
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2
7
10
14
18 unbalanced
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