9 Jan
2017
9 Jan
'17
9:33 a.m.
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! Jim Propp