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Since we're arranging squares, I'm assuming the arrangements are all going to be only two-dimensional and no stacking is allowed. If you have played tetris before, you'll know that can be arranged into :
1) A straight line
2) A 2 by 2 square
3) A T-shape
4) A L-shape
5) An inverted L-shape
6) A ladder
7) An inverted ladder
That's all the seven different arrangements for four squares.
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i
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