Message #2695

From: schuma <>
Subject: Re: Halfcut 120-cell
Date: Wed, 20 Mar 2013 07:51:38 -0000

— In, Melinda Green <melinda@…> wrote:
> How would you even start to develop a solution?

This puzzle is special in that there is no anchor in the cells that tells you the eventual colors. Andrey, here’s a question for you: do we have to solve the puzzle with the original color scheme, or any color scheme is fine? I think only you can answer this question… Let’s forget about this issue for a moment.

If I were to solve it, I would commute the twists around almost-antipodal cells. This puzzle is a half cut puzzle, so if A and B are twists around exact antipodal cells, then A, B, A’, B’ does nothing: there’s just no overlap. But if A and C are twists around almost-antipodal cells, the regions they move has a thin layer of overlap. Then A, C, A’, C’ moves a few pieces. related to that thin layer. Then I would probably look for another sequence D as setup (sequence = D A B A’ B’ D’), to move most affected pieces into one hemi-hypersphere, and only leaving a few (ideally one) in the other hemi-hypersphere. Then commute the existing sequence with a twist that turns the latter hemi-hypersphere to eventually construct a three cycle.

Then I will think about a good order to solve the pieces. This step may be the trickiest one for this puzzle. When you try to sort 14,400 things, you’d better have a good plan.

Once I have a plan, I will make a lot of variations of three cycles with different setup moves to build my library of macros. Using this library, I should think only very little to execute the plan.

Then I would try solve some pieces to polish the plan. Solve five pieces in a row, and see how long it takes. If we can get to one minute per pieces, we will need 240 hours. If we are OK with working on it 3 hours a day (which is hard to maintain in long term), it takes almost three months. If our strategy is really good and takes half a minute per piece, it’ll still take at least one month.

Before even start the solve, I would write some script to monitor the log file and print of percentage of completion. Every time I solve a piece, this number will increase by around 0.01% on average. During my solve, I would keep keep looking at this percentage and timing myself. I would probably set a daily goal of 1% every day to keep myself motivated.

After three months or even more, I come here and announce it has been solved.

Yeah, this is my plan. Well, I don’t really plan to solve it…