Here is a problem:
Given N > 1 squares of arbitrary sizes. Is it always possible to dissect the squares into pieces that will combine (without overlapping or holes) into a bigger square?
For N = 1, the question is vacuous. For N = 2, we actually have several solutions. The keyword here is the Pythagorean Theorem. Solutions ##2, 3, 4, 14, 15, 26, 27, 28 all show different ways to cut two squares into pieces that combine into a single square.
What about larger N? The answer is yes, of course. To solve the problem for
- G. N. Frederickson, Dissections: Plane & Fancy, Cambridge University Press, 1997
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