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?...