Various numbers get bandied about. 10^{120} seems to crop up a lot.

As far as I can see, 13^{64} (Fermat's Last Pizza) ought to be the upper bound (that's about 10^{71} ) - and that includes boards with way too many pieces.

This thread - http://www.chess.com/forum/view/general/how-many-different-chess-positions-are-there - discussed an approach for calculation based on enumerating sets of valid pieces (e.g. 2 pieces: 2 kings; 3 pieces: 2 kings + white pawn; 2 kings + black pawn; 2 kings + white bishop, etc.) all the way up to 32 pieces.

Ziryab wrote: If you google "chess position statistics," you should find the website of François Labelle at UC Berkeley who is working on computer modeling and mathematics and has an interest in chess. You'll see that he is carrying Claude Shannon's research much further.

According to Labelle, there are no more than 10^{50 }distinct board positions.

I'm not sure if this is the right place to post the question.

How many ACTUAL chess board configurations are their? I HAVE been able to find sites with answers to this question that include boards with extra pieces (like a board full of white Kings) (http://ioannis.virtualcomposer2000.com/math/EveryChess.html), but this is not what I am asking. There can

notbe extra pieces.It is OK, however, if one or more of the board configurations in the answer would be impossible to get to in a normal chess game.

So, to sum up:

- Total number of possible chess board configurations.

- Using

at most1King,1Queen,2Rooks,2Knights,2Bishops, and8Pawns. (blackandwhite).- Some Impossible boards are OK (such as a board with no black king, or any board that could never happen in a normal game.

Even boards with overlapping pieces would be OK I guess, although not preferred).BONUS: If you can exclude impossible boards in the answer, more power to you!