# Original Art by Ian P. Hudson — Squares

## Squared Squares

These paintings are inspired by the minimal* solution by A.J.W.Duijvestijn (in 1978) of the “squared square” or perfect square dissection problem — dissection of a square into smaller squares all of different sizes, and with no subset of them forming a rectangle.

My own mathematical contribution was to find a colour scheme such that the 21 squares form six sets each of a single colour, the sets comprising respectively 1, 2, 3, 4, 5, ∓ 6 squares, such that no squares of the same colour have a common border. In my chosen solution, the smallest square is the sole member of its set**.

* “Minimal” means that there is no solution with fewer than 21.

** I invite mathematicians to try to prove or disprove that this is true of every such colouring solution for this 21-square dissection!