Consider packing N unit squares into a square of side 2 such that the small squares are orthogonal and centered at coordinates 0.5, 1, or 1.5.
0 squares = 1 possibility
1 square = 9 possibilities
2 squares = 8 + 4 + 2 + 2 = 16 possibilities
3 squares = 4 + 4 = 8 possibilities
4 squares = 1 possibility
Total = 35 ways including empty, a surprisingly large number.
Inspired by recursive characters.
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