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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