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U turn sans U turns

Submitted by B MacKenzie on Thu, 08/21/2008 - 22:28.

All elements of the Rubik's cube group may be generated using turns of only five of the six faces, say all but the Up face. This suggests a puzzle variant: a cube with the Up center cubie glued fast. Has any work been done on such a puzzle? I played with this a bit today. Here's an U turn macro using no U turns:

B D' F L' F' B D F' R B' L F' D F B' L' F

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There are shorter maneuvers f

Submitted by kociemba on Fri, 08/22/2008 - 06:59.
There are shorter maneuvers for this (in the face-turn-metric):

L R B2 F2 L' R' D L R B2 F2 L' R' (13f*)
L R' B2 F2 L R' D L R' B2 F2 L R' (13f*)

You can generate them directly with Cube Explorer with a little trick.

1. Gray out e.g. the UF-edge cubie of a clean cube by right clicking in the Facelet Editor.
2. Make an F(!)-turn with the "Apply Move" button.
3. Press "Add and Solve".
4. A maneuver window appears which generates solutions.
5. Stop the search.
7. Check the F-box in "Faces to exclude".
8. Press "Add and Solve" again. Now only solutions which generate the F-turn without using the F-face are generated.
9. "Add solutions to Main Window".
10. To get the solutions for U-Turns Right click on each cube and "Rotate 1/3 about URF corner".
11. File|Save Maneuvers.
12. The textfile contains the generators for the U-Turn.

In a similar way I got for example the "Cube in the Cube" pattern without an U-turn in 16 moves

R' D' L D F' R2 D' F D2 R B2 R' D L' D2 R (16f*)

For random cubes this method might be too slow, because the module for solving incomplete cubes has only small pruning tables.

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re Five Face Puzzle

Submitted by B MacKenzie on Fri, 08/22/2008 - 15:35.

Seventeen is the optimum in the q-turn metric. When I started to consider this I put together a macro composed from several edge+corner double swaps and it took me 87 q-turns.

I have since disabled one face turn and solved several random cubes manually. It turns out not to pose that great a handicap, a least not with my method. I average 85 to 90 q-turns normally and disabling one turn adds maybe 10 to 15 turns extra.

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I remember reading an old book

Submitted by jcm on Tue, 08/26/2008 - 05:14.
I remember reading an old book (probably in 1983) on the Cube that displayed this trick, and the maneuver had the name of its discoverer, but I don't remember what it was.
The solution was the second one submitted by Kociemba.
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