Received: from MC.LCS.MIT.EDU by AI.AI.MIT.EDU via Chaosnet; 6 NOV 86 15:06:54 EST Received: from nrl-aic (TCP 3200200010) by MC.LCS.MIT.EDU 6 Nov 86 15:02:30 EST Date: 6 Nov 1986 13:41:48 EST (Thu) From: Dan Hoey Subject: Magic To: Cube-lovers@mit-mc.ARPA Message-Id: <531686509/hoey@nrl-aic> I have three macros for transforming 2x4 rectangles. To solve the puzzle, I use two of them followed by a seven-flip macro that changes a 2x4 shape into a 3x3-1 shape (beats me how BECK can call this a ``2x3x3''). Took me a couple of half-days to solve it. I have found 32 different 2x4 rectangles. I think that is all of them, but I haven't got any proofs, nor even a decent mathematical model for deciding when a flip is possible. I am trying to understand how the strings work. First, it looks like there is twice as much string as necessary; each string is doubled. I guess that this duplication has no effect on the puzzle except for durability, but until I can dyke one out can't be sure. I'm concerned that the string may be one double loop, so I'm looking for a good way to make sure the thing doesn't unstring entirely when I cut one. Each side of each piece has four short channel segments and four long; half are occupied with string. If you continue each segment across each hinge to the next piece, you get eight channels composed of alternating long and short segments. Again, four of the eight channels are occupied. In the positions I've seen, each of the channels contains eight pairs of segments. But Magic is more complicated than that--the strings do not always follow a channel from piece to piece. On half of the pieces, there is an extra loop of string that wraps back onto the piece without following the channel to the next piece. I don't know what function this serves. If a good model of the string interactions can be developed, we may be able to make an attack on the doughnut problem based on the length of string channels. In the doughnut, there are four ten-pair channels and four six-pair channels. We may be able to show that the string wouldn't reach one, and would exceed the other. More likely, the model will prohibit the doughnut more directly. There is another string-related question I am wondering about. I have noticed some of the string-pairs getting twisted. I wonder how bad this can get. Does anyone have an operation that can be repeated to make the twists tighter and tighter? Are these puzzles built for obsolescence? I have been considering Magic metrics, but it's a difficult problem. Counting flips is easy enough, but how do you count a move that skews a parallelogram? Are such skew moves necessary? Dan