So, I was recently given a cube, which once again sparked my interest
in the whole thing, however it appears that the stickers have been
pulled off and re-arranged at some point. (The faces don't match any
I've seen mentioned in the archives or the various web pages.)

Which doesn't necessarily mean it was attacked by a mad sticker-moving
artist; it could just be an off brand. :-)

What would be the right way to put it back together to get a
"working" cube?

Well, first I'd try solving it and see if I end up with something like
two edge cubies colored the same, or a corner having colors that belong
to opposite center cubies. If no such problem is found but a parity
constraint is violated (eg, a single edge cubie flipped), it was just
taken apart, so I'd take it apart and put it back together solved. If
I _do_ find an "impossible" cubie, then I'd just take the stickers off
and put them back on such that every face is a solid color. (I'd
probably try to mostly-solve it first, so's to minimize the number of
stickers that need moving, but that's a frill.) If you take all the
stickers off, all states are the same; there is no mechanical state you
have to match when putting the stickers back on.

der Mouse

mouse@collatz.mcrcim.mcgill.edu