Message #580

From: mshaw@math.utexas.edu
Subject: Re: [MC4D] A new record for the 5^4 checkerboard! Sorry Remi!
Date: Sun, 21 Sep 2008 18:26:23 -0500

Dear Remi (et all),

So I guess it’s time to have a history of the checkerboard solutions added
to your hallofshort.html! What a freak coincidence! The actual
accomplishment took place on the 19th not today, but I wanted to wait a
couple days in case some obvious improvement came forth.

REMI:
> I just checked the email to find your post :) First the all:
> CONGRATULATIONS! After beating my record in 3^4 I spend some time
> analysing your solution and I hadn’t found much joy in only slightly
> improving your solution (It’s funny that you say that you learn it how to
> improve your solution analysing my previous solutions).
> I’ve tried to implement my final result from 3^4 to 5^4 but I failed…
> (I’ve tried for at least one week so I spend some time on it…)

Wow! I’m really shocked! Consider the canonical embedding of the 3^4
into the 5^4 cube. That is ignore all pieces except the pieces you see in
3^4, (for each color combination) only one 3-color piece instead of three,
only one 2-color piece instead of nine, only one 1-color piece instead of

If you do this then, 2-twists don’t matter, only 1-twists and
3-twists matter. Now look at your 5^4 solution and treat all 3-twists as
2-twists on the 3^4 cube.

Interestingly, I recreated your 5^4 solution without viewing yours (since
last year) only by listing my 3^4 solution up to 5^4 applying the secret
algorithm twice with two different embeddings. These can best be seen on
the rubix professor and then listed to 4-D. One is restricting to
1-twists as in the typical final steps of the 5^3 solution. The other is
restricting to only 2-slices (i.e. simultaneous 1-twists and 2-twists).
You will see that the mathematical structure of the 5^3 with either of
these restrictions is the same as that of the 3^3 rubix cube.

And then, of course, broke your 5^4 record by lifting your 3^4 record,
improving it in the same manner you improved mine!

Well now I’m glad I didn’t tell you how my solution was lifted from yours,
so that I could steal your 5^4 record before you improved it yourself. lol
sorry you spent so much time on it. You really deserve the credit! And
you will always have the FIRST :)

I have so much to say about my background/introduction :), about
subgroups, symmetry groups, and comments on many of the previous posts,
but this will soon come.

Peace and Love,
Markbob