Wonderful questions. The second question lends itself to an especially nice presentation: use all these pieces to make exactly three squares. Then use the same pieces to make exactly four squares. The best version would have a unique solution for each of these challenges. Presentation for the first question is siimilar: use all these pieces to make exactly four squares. Now find a different solution. If no one has a dissection for these challenges, then I'm going to look for a minimal one. On Mon, 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!
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun