
The big 13x13 square can be
dissected into 11 squares as shown in the illustration above. We
can see:
2 squares 1x1,
3 squares 2x2,
2 squares 3x3,
1 square 4x4,
2 squares 6x6, and
1 square 7x7.
This is the only solution with so few single squares, and this is the
minimum that can be reached for the 13x13 square.
It's a really hard puzzle nut. If you make a set of the 11 single
squares shown above (simply
print them and then cut 'em
out) and propose to your friends to assemble into a 13x13 square,
you'll see that even so this new puzzle will be amazingly hard to do.
We've received many solutions with 12 squares, and some solutions
with... 1 square 13x13. Apparently the last one is wrong, as in the
description we told that:
"The big 13x13 square shown in the illustration can be dissected into
some number of square pieces (cutting along the lines only)."
Also one solution contained just 4 squares, but they are overlapped,
so their total area is not 169 but 170. This isn't acceptable as the
description says:
"... your set MUST fully cover the 13x13 grid without gaps or
overlapping." 
