Oct 11th 2000 - Cut a square...
Cut an integer square into N pieces and build three different squares.

N = 10

This is an example with N=10. I asked to minimize N and the solutions are soon arrived. Below there is a nice simple solution:

7x7 = 6x6 + 3x3 + 2x2

In the original example I did 3 squares with irrational edges from an integer square. Then I asked to minimize N also for these rules. Below there is my solution:

My solution with N=7

I thought seven is the minimum, when Paolo Licheri, with a little help from Dario Uri, surprises me with his N=6 solution.