How to square a square? How can you devide a square into smaller square which are all different?
Seems simple. We had seen an old solution from 1956 ... but still it took us 15 years to find the first few ourselves.

While working on imperfect squares, we expected to find the perfect ones automaticly. Via the perfect rectangles (which algorithm is more accurate for this purpose) we finally did. Hard to believe that there will exist probably infinite solutions! The 110-square is the smallest known, but not proven yet to be the smallest possible. We are quite certain that the smallest possible is at least 110x110, Unfortunately our algorithm is still much too slow for the larger puzzles (above 130).

110x110 puzzle, 22 squares.
Working with a large square (60x60) we didn't expect to find a perfect solution. We found two!

110x110 puzzle, also 22 squares.
Very simular to the first one.

110x110 puzzle, with 23 squares.


112x112 puzzel, with 21 squares.

Mathematicians proved that a solution should exist of at least 21 squares (with only one solution). All other solutions will have 22+ squares.

Links:

squaring.net. Duizenden perfecte vierkanten en rechthoeken!
Mathworld - Perfect Square Dissection