Message #1380

From: Brandon Enright <bmenrigh@ucsd.edu>
Subject: Re: [MC4D] Variations of Rubik’s Cube puzzle
Date: Thu, 03 Feb 2011 20:46:28 +0000

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On Thu, 03 Feb 2011 02:42:40 -0000
"puzzle314" <puzzle314@yahoo.com> wrote:

> but intermediate, advanced, master
> and grandmaster levels are very complicated. It appears easier to
> create than solve these puzzles. I would really appreciate if
> somebody could find solutions and send me the algorithms for these
> three levels.
>
>
> Alex

Hi Alex,

It’s great to see people continuing to innovate in the world of
twisty/flippy/slidy puzzles.

For your beginner puzzle, I would commutate a 2-gen, 3-move
sequence to achieve a 3-cycle. This is 8 moves and it cycles 3 squares
pure. That is, 3 moves, 1 move, undo first 3, undo 1 move. I haven’t
tried solving it intuitively.

I think your intermediate puzzle is much easier. Only 8 moves are
possible, 2 in each of spots {4, 7, 10, 13}.

Unfortunately I’ve noticed a couple bugs. First, "start new" only
scrambles the puzzle with horizontal flip moves. Second, "start new"
applies the scramble to the existing puzzle state so if you do a V
move and then scramble more states are available to be solved. Third,
you recognize any solution that groups the 4 solid colors into squares
as a solve rather than the original state.

Ignoring those problems, use intuition to move the yellow and blue
pieces to the top half and the red and green pieces to the bottom
half.

Then using only H moves in the 4 and 7 spots, form at least
one solid square in the bottom half. This takes no more than 2 moves.
It doesn’t matter if you form two squares or 1 square in the middle and
two columns on each side.

Then using only H moves in the 10 and 13 spots you can form at least
one solid square in the top half.

If the bottom half in one square in the middle rather than two squares
use V7, H13, H7, V7. This only has an effect on one half. Obviously
via rotation or mirroring you can use it to fix the top half too.

As it stands right now with the limited scrambling and the multiple
solved states I think "god’s number" on this puzzle is 7 or less.

Brandon

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