# Message #2199

From: schuma <mananself@gmail.com>

Subject: Re: Making a puzzle based on 11-cell

Date: Fri, 25 May 2012 19:24:12 -0000

I haven’t explained how the text input/output function works yet. Let me do it now.

When you make some turns, you’ll notice some characters are generated in the text output box. You can ctrl-A and ctrl-C to copy them out. When you ctrl-P them into the input box and press the "input" button, this sequence will be executed again. You can also edit them in any editor.

Here’s the meaning of the sequence: each twist is represented by three characters. The first character may be A~K or a~k, representing which cell is turned. An uppercase letter means it’s a normal twist. A lowercase letter means it’s a whole-puzzle twist. The second character may be V, v, F, f, E, e. It means the axis passes through a vertex, or a face, or an edge. Uppercase = CCW (left click), lowercase = CW (right click). The third character can be 0~9 or A~E. It’s an internal ID for a vertex/face/edge on each cell. Even I don’t remember which number stands for which object. You may put any separator between the three-character triplets, "," ";" "(" space newline etc. All of them will be ignored.

For example, "AV0" means turning around cell-A (the red cell), on vertex number 0, CCW. Inverting a move can always be done by changing between upper case and lower case of the second character.

——— here comes the story of solution ———–

Using this text input method, I studied the algorithms.

2C face pieces: permutation is always even, and two 2C pieces can be flipped at the same time. There’s [1,1] commutator. So solving the permutation is intuitive.

The orientation of 3C edge pieces behave like in MC4D: two edges can be flipped, each like (a,b,c)->(b,a,c), and a single edge can be rotated like (a,b,c)->(b,c,a). I conjecture that single-edge flipping like (a,b,c)->(b,a,c) is impossible, but I just haven’t got a proof yet. I need to count the parity of edge stickers of a twist to prove it.

For the 6C vertex pieces, each can be rotated in place in many ways. The six stickers are always in even permutation. I’ve seen a 5-cycle, or two 3-cycles, or two 2-cycles. But the group A6 is simple, so there should be an algorithm to do a 3-cycle. But I haven’t found it yet.

After the preparation, I started to solve it. 2C pieces are mostly solved intuitively (I consider [1,1] commutators are intuitive). 3C is the most tedious step. When solving 3C pieces, for example, I have a cyan-blue-yellow piece, then I need to find the destination of it. To do that I hold ctrl and hover the cursor around the the cyan cell, and look at the blue and yellow cells and check when there’s a circle in each of those two cells. Once I found the destination, it doesn’t take more than two or three setup moves to bring it to the 3-cycle working spot.

There’s an episode here. I had a cyan-yellow-brown piece. When I looked for its destination, I found there shouldn’t be such an edge of this color combination. I was nervous because there must be a tricky bug in my code creating the "invalid piece". It would be very hard to repeat this bug. I was thinking about how to validate the moves to catch this bug. I thought a lot, then I realized "brown" is actually purple. It was just the edges are so narrow that it was hard to distinguish a foreground colors with the presence of a colorful background. Roice warned me about it, but I haven’t changed it yet. After the solution I made the edge wider.

6C pieces are not that tedious. There are only 11 of them. For permutation, I have a 3-cycle algorithm. For orientation, I have an algorithm to do two 3-cycles for the six stickers on one piece. I just use that orientation algorithm again and again to solve all the cases.

That’s the end of the solution. I’m going to add a dialog to warn the solver because clicking reset during a formal solution. Currently if I misclick the reset button in a solution everything will be lost. This is something I noticed in my solve.

Nan

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:

>

> Congratulations, Nan!

> Please tell us the story of your solve? Most of us will never attempt a

> solution so we must take our enjoyment vicariously from the descriptions

> of others. In particular, I wonder how it compares with solving puzzles

> that make more sense visually. Or should we expect it to be as

> inconceivable as an 11 dimensional puzzle? Inquiring minds wish to know.

> -Melinda