Message #2968

From: Melinda Green <>
Subject: Re: [MC4D] RE: 120Z solved!!!
Date: Sat, 08 Mar 2014 03:16:36 -0800

That’s a wonderful puzzle story, Nan. Congratulations! In the middle, I
believe you said it’s the hardest puzzle you ever attempted, right? It
certainly sounds like a bear! Is anybody else working on it or thinking
about it? I may feel as frightened of it as other people are of MC4D
when I describe it to them. I often don’t have the heart to tell them of
all the other crazy puzzles we deal with. The human mind can take only
so much amazement at one time.

I don’t think you should feel disappointed by having used computer
assistance, especially because you wrote the code. That code is an
extension of your mind and required you to understand what you wanted it
to do which tells me that with sufficient time and patience, you could
in theory have performed it all by hand. Don Hatch wrote a program to
solve the 2^d and 3^d cubes in all dimensions > 2 I believe. I therefore
believe that he has solved them all, just not in the same way as human
solutions. This is by the same extension that we consider macro
solutions to be completely valid too, just not comparable to no-macro

I am particularly curious about that 3C stage and wonder whether it
might suggest a much smaller puzzle with the same sort of difficulty.
Can you think of a 3C-only analog puzzle that requires a similarly deep
dive to solve but perhaps not involving so many cells? For instance, how
does this step compare with, say, an edges-only version of the 24Z? Or
MC4DZ, or even a 3D Void Cube
<> Z for that matter?

Now that I look at that last puzzle I realize that it looks and turns
exactly like a subset of MC4D! I want one! It looks simple but I expect
that a Z version would be much more difficult if it were somehow
possible to build.

So what’s next for you, Nan? Some time outside in our lovely pre-spring
weather perhaps?

On 3/7/2014 11:15 PM, wrote:
> Finally, I’ve solved the 120-cell Mirror Z. It took me 357330 steps
> (happen to be an even number!). The game clock shows 38 hours and 45
> minutes.
> As mentioned earlier, I used some script to analyze the orbits. I
> found that after solving the 3C pieces, all 2C orbits are evenly
> permuted. So, as planned, I solved 3C first, then 2C, then 4C. 3C took
> about 19 hours and 85k moves; 2C about 2 hour and 24k moves; and 4C
> about 17.5 hours and 248k moves. 2C pieces were indeed easy after 3C
> were solved.
> I have to admit that this time I went too deep using computer. I used
> a parity fixing strategy found by the script for 3C orbits: flipping
> 19 cells changes the parity of seven 3C orbits which pass through one
> cell. This is the most powerful 3C parity algorithm I’ve found.
> Without computer I’d have a hard time finding such 19 cells. I used
> this algorithm several times towards the end of the 3C step. I’m
> certainly not proud of it. But it’s hard not to look at the 19 cells
> when the script has already generated it.
> As before, I used a monitoring script to keep track of progress so
> that I know it when I screw up things. I also used Git to backup the
> macro and log files.
> Scripts and files are dumped into this github repo:
> I’ve never organized the script though…
> Andrey, thank you for making this puzzle! Also, if you didn’t solve
> the puzzle, I wouldn’t even know how delicate this puzzle was and I
> wouldn’t even attempt it.
> Nan