# Message #3090

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

Subject: Re: MagicTile Solving

Date: Mon, 23 Mar 2015 14:21:15 +0100

It is not easy at all to find "new colorings" in MagicTile. I once tried it with the help of the MagicTile programmer (Nelson). Interested persons can get instructions from Nelson. So it is not astonishing that a conceptor of new MagicTile puzzles cannot predict what eventually fascinating laws a solver will find in the unexplored world of a newly created MagicTile puzzle.

I have started to solve my 3rd MagicTile this year. It is "MagicTile hyperbolic {10,3} 6 color vertex turning 0:0:1". I have already solved tha same puzlle with 12 colors (instaed of 6) about two years ago with 18ā000 twists. You have to know that MagicTile puzzles can get seriously more difficult if you diminish the number of colors because the place for manoeuvers gets narrower. "MagicTile hyperbolic {10,3} 6 color vertex turning 0:0:1" has the following pieces: 1-c corner-faces, 3-c vertices, 1-c edge-faces and 1-c faces. Correspondingly you can separate the puzzle in four stages. Normally the first stages are easier to solve. I have not yet finishes the puzzle. But already now as I have solved only 2 of 4 stages I have over 11ā000 twists and plenty of experiences to tell from.

(a) Stage "corner-faces". Despite of the fact that the pieces are 1-colored the solving is not easy at all towards the end. You have to fight against "orbits".

(b) Stage "vertices". Already the counting of the different vertices is not easy. There are exactly 20 pieces organised as 10 pairs of twins. After having constructed macros for a 3-cycle for placing the vertices and for the rotations of a pair of vertices and after having applied those macros I was left with 12 of 20 vertices in a mirrored orientation. To get a mirroring of two twin vertices you have to interchange the places of the wtin by traversing the whole puzzle (non-orientable, Klein). Iām very proud to have succeded to consruct a macro which does the mirroring of 4 vertices together with the rotation of another single vertex.

And now I will enjoy the next two stages.

In the pictures I show (1) the puzzle with the different kinds of pieces, (2) the effect of the cornerface macros, (3) the effect of the vertex macros and finally (4) the vertex mirroring.