# Message #1235

From: Andrey <andreyastrelin@yahoo.com>

Subject: Parity in 12 Colors

Date: Mon, 01 Nov 2010 17:51:32 -0000

When I almost solved 12 Colors puzzle I found unexpected parity problem: one 3C piece had wrong orientation (transposition) and two 4Cs were swapped. I’ve never seen anything like that before (close situation is on 4^3, but there is transposition of 2Cs instead of flipping, so it’s different). Closer inspection shown that the problem is in the number of 3Cs in one cell: it’s odd (27). So 60-deg rotation had chance to flip orientation of odd number of 3Cs. On other hand, this rotation gives even permutation of 2Cs (6+2+1 cycles), and parity error can’t be detected on the first stage.

This problem took about 500 extra twists, and puzzle was solved… in 4196 twists (no macros!) and 12h 00m 00s.345 (by timer) :) A little long - but I’m not sure in Undo/Redo operations and used to make back twist instead of Ctrl-Z.

My solving method is close to speedsolving 3^4 algorithm - it uses the fact that there are two cells with no common pieces. So for 8Color and 14Color this method doesn’t work.

It looks like 1.0 version will be not very soon :( - mathematics in MHT is very complicated (mixed Complex-Modular arithmetics) and some hidden bugs may remain hidden for a long time :(

Good luck!

Andrey