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 Post subject: Pillow Cube Query
PostPosted: Wed Jul 04, 2001 2:32 am 
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Joined: Sat Dec 02, 2000 8:27 pm
Location: Wilmington, NC, USA
Can anybody recommend a solution for the pillow cube? I have two adjacent "edge" or shaved pieces on the same side of the pillow that need to be swapped. This should be impossible on a regular cube, but I have a sneaky suspicion that this condition is okay on the pillow cube. Does anybody know who invented this puzzle?


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 Post subject: Flip another piece
PostPosted: Wed Jul 04, 2001 12:09 pm 
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Joined: Fri Dec 08, 2000 2:32 am
Location: San Francisco, CA
On a 3x3x3 cube, you can't flip a single edge. On the Octagon and Pillow, however, some pieces are indistinguishable when flipped.

Just pick one of the shaved edge pieces and perform an operation from one of the many published solutions for the 3x3x3 which flips that piece (no visible change) and the one that's "visibly" flipped.

Take heart - at least it's not an Alexander's Star (or similarly elaborate polyhedron), where it's trickier to flip an arbitrary piece when the rest of the puzzle is nearly solved. On the Pillow it should be a single turn to get a shaved edge and your flipped edge ready for a monoflip operation.

Speaking of the Pillow, anyone have one they want to part with? I can offer a Mystic I.Q. Ball in trade, and possibly connive a Dogic (12-color) if you sweeten the offer a bit.


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 Post subject: Swapping pieces
PostPosted: Sat Jul 21, 2001 5:09 am 
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Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
Joshua, Carter wanted to swap two pieces, not flip one.

I don't have a pillow, but I don't think this is possible from the pictures I have seen. The middle layer pieces are all in positions fully determined by the colours of the centres. The pieces on the top and bottom faces may be swapped, but this is an even permutation which will not help in swapping a single pair.
The only other possibility I can see is that 4 of the centre pieces have the same colour, in which case you can do a slice move in that plane (an odd permutation on pieces since centres are indistinguishable) and solve it again.

Jaap's Puzzle Page:
http://www.org2.com/jaap/puzzles


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 Post subject: Pillow Solution
PostPosted: Sun Jul 22, 2001 5:09 am 
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Joined: Sat Dec 02, 2000 8:27 pm
Location: Wilmington, NC, USA
Jaap, I think you are correct. There are three white center squares. I think it might be solved by "turning it inside out" or switching the top to the bottom. Actually I tried to do this a couple of times and ended up with a total mess and had to start all over. My hands wore out before I finished it. In the end, I traded the puzzle to a good home, where it won't need its old stickers, anyway.


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