Here's a question for y'all.....
It's about the tetrahedron puzzle from Rubix (I forget the real name).
[the one with legal moves consisting of removing a 4-piece tetrahedron from
a 10-piece and putting it back on in different orientation]

Anyway, mine is pretty loosed up, and occassionally when I am working on it,
one piece will come loose and go skitting across the floor.

There's no way I can remember the orientation it had on there. Has any study
been done or does someone know if I put that piece back on, will it still be
solveable if it's orientation is wrong (ie, different than it was before it
fell off)?

Do you understand my question? (I hope I'm not too confusing...)

I've been thinking about implementing this via computer, just to test this
out, but I thought I'd ask y'all first.

Thanx.