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Mathematics has played us for absolute fools
If you can put the diagonal squares from the 17 solution in a 2-3-2 configuration, I can almost see a pattern. I wonder what other configurations between 17 and 132 have a similar solution?
Why can't it be stacked up normally? I don't understand.
You could arrange them that way, but the goal is to find the way to pack the small squares in a way that results in the smallest possible outer square. In the solution shown, the length of one side of the outer square is just a bit smaller than 12. If you pack them normally, the length would be ~~larger than~~ exactly 12. (1 = the length of one side of the smaller squares.)