# Message #2890

From: mananself@gmail.com

Subject: Re: [MC4D] RE: MPUltimate 1.5

Date: Sat, 18 Jan 2014 11:42:05 -0800

I just solved the 24-cell Mirror Z puzzle. It took me about 5.8 hours according to the timer in MPUlt, and 55231 moves. I used about the same number of moves as my solution of the original 24-cell puzzle. And I don’t think I’m very careful about shortening the solutions on either puzzle.

The most interesting part of this puzzle is the 2C face centers. It’s quite obvious that there are 96 such pieces in total, divided into 16 orbits. And it’s trivial to do 3-cycles in each orbit. But managing the parities across the 16 orbits is not trivial. You cannot just change the parity of one orbit, neither can you change two orbits at the same time. You can change the parities of four orbits (any move does that), or six orbits in certain configuration. It has to do with the geometry of the 24-cell. I enjoy thinking about it. I guess the mirror Z 120-cell has a similar situation with 2C pieces, but it’ll be too tedious to analyze.

Solving the small pieces around vertices was just tedious and less challenging.

Thanks for making the puzzle!

Nan