# Cutting Squares

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

### Reference

- G. N. Frederickson,
*Dissections: Plane & Fancy*, Cambridge University Press, 1997

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