I like this, too. As usual, I'd find it even more elegant to see a minimal geometric dissection of a small collection of integer-sided square *tori* into another collection having the same total area. For equal sums of nth powers, the same question for cubical n-tori. E.g., ----- What is the minimal dissection of cubical 3-tori of sides 3, 4, 5 into one of side 6 ? ----- —Dan
On Jan 9, 2017, at 8:33 AM, James Propp <jamespropp@gmail.com> wrote:
Has anyone devised a fun puzzle in which a 1-by-1, 4-by-4, 6-by-6, and 7-by-7 square are divided into smaller polyominoes which can then be reassembled to form a 2-by-2, 3-by-3, 5-by-5, and 8-by-8 square?
(The title of the thread is a variation on Matt Parker's "Share the Power" puzzle, which is a generalization of this to higher powers, but without the embodiment via polyominoes.)
My guess is that the best puzzle of this kind (i.e., the most challenging to solve) would be one that used a near-minimal number of pieces.
I'm also seeking a polyomino implementation of the identity 0^2+3^2+5^2+6^2 = 1^2+2^2+4^2+7^2, though of course one of the squares has vanished!