From Don.Woods@eng.sun.com  Mon Jan  3 17:11:06 1994
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Date: Mon, 3 Jan 94 14:11:09 PST
From: Don.Woods@eng.sun.com (Don Woods)
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To: cube-lovers@ai.mit.edu, jandr@xirion.nl
Subject: Re: 10x10 Tangle
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> >It's a shame, really.  I'll bet that it would be possible to come up with
> >four Tangles that (a) really are different instead of being simple color
> >permutations of each other, ...
> 
> When you limit yourself to 4 ropes with 4 colours, you always get 24 pieces,
> and when you want to build a puzzle of 25 pieces, you will have to duplicate
> one, which causes (a).

Not so.  There's nothing that says all permutations must be present.
Back in '92 when I first wrote the program to solve Tangle #1, I fiddled
with it a bit and found that removing a particular tile and adding a
duplicate of a second particular tile caused the solution to become
unique.  It didn't take long to find such a combination, so I'm confident
there are many many more that have unique solutions.

Hm, using just the set of 24 distinct tiles, I wonder if it's possible to
tile the faces of a 2x2x2 cube such that colors match at the edges of the
cube as well as within the faces?...

	-- Don.