# Message #3568

From: Eduard Baumann <ed.baumann@bluewin.ch>

Subject: MagicTile few colors

Date: Fri, 18 Nov 2016 12:56:14 +0100

Hi Mike and Roice,

I said that I don’t like much the magictiles with few colors. I use a method where I compose a toolbox with 3-cycles for every piece type and orienteering manoevres on place. In few color puzzles such 3-cycles often cannot be found. We enter the domain of very finite groups and this can be very hard. Do you know the Mathieu groupe m24? I takled this groupe in 2008. See http://www.baumanneduard.ch/m24%20aw%20table.txt, www.sciam.com/article.cfm?id=puzzles-simple-groups-at-play

Some few color magictile can be solved whitout havy work with intuitive heuristc technics. In the magictile "ell sph orbifold 3-4 4B f0-0-0,8 v0,8-0-0" I have the following situation. After 93 twists I’m finished with faces, corners and edges. I’m left with a 8-cycle of the tiny edge2 pieces. To better understand things I change the settings to "foundamental view only". Here it is not easy to see that there are only 8 different edge2 pieces. On the other hand we have only 2 different corners with 2*3 twists and 4 faces with 4*2 twists. That are 14 twists only. I have macro which can do a double edge2 exchange (4 pieces involved). What I can do now is: try all 14 setups to my macro and note the resulting permutations, generate with those all possible permutations, find the 8-cycle with which I was left. Conclusion: Mike, you have solved this puzzle with very few twists, how are you working ?? Without help of programming ??

Kind regards

Ed Baumann