Hello all,
Aha! I did make a mistake, as I suspected I might have. It's been too lon=
g since I counted permutations. :) My previous answer was off by a factor =
of 2; the 2 in the denominator should not have been there. I made the clas=
sic mistake of taking even permutations into account when there are identic=
ally colored pieces (in this case, stickers). Naturally, with identically =
colored pieces parity does not matter, as even and odd permutations are ide=
ntical.
Here is the correct formula and number of permutations:
209!/(((7!)^29)*(6!)) =3D
298225837482940676509184100728720811004423111510479240177876435252200583634=
046383785012187494718519005671580310160782720965515620763618140216746589818=
598244298634557645722755900360127929767933245249492609612953156836861423588=
4567287678429277548260303941234016334643200000000000000000000
My apologies for not catching this sooner; I've been very busy today with e=
mails. I am virtually certain that this count is correct, as I just sent R=
ay a complete derivation of it (which is how I discovered my error).
Thanks to everyone for your patience, and I'll keep you informed of my prog=
ress.
All the best,
David