Cluemeister's Corner
December Puzzle: How Many Chess Moves Are There?
December is a good month for playing chess while surrounded by opulent decorations and plentiful victuals. Here's a conundrum you may have wondered about if you've ever learned the algebraic notation system of recording chess games. How many different moves are possible within this system?
Various web sources purport to say how many chess moves are possible (including the excellent Tim Krabbé's Chess Curiosities), but they appear to either be counting the number of possible positions (something quite different) or to be taking into account both the initial square of the piece and its destination. But this is long algebraic notation, while the World Chess Federation (FIDE, from the French) requires the use of short algebraic notation, which omits the initial square. So far as the Cluemeister can tell, no one has ever calculated how many distinct FIDE notations are possible, so he determined to figure it out himself. Can you do better?
As with our September question, a few clarifications are needed. The FIDE Handbook, with a full description of the notation system, can be found here, but the relevant points are addressed below…
- Draw offers ("="), final results ("0-1"), and notation evaluating the quality of moves (such as "!?") are not here considered part of algebraic notation.
- Checks ("+") and checkmates ("#") are recognized; double check ("++") is not.
- No hyphen is used to separate the moving piece and its destination—"Nb3" is used rather than "N-b3". (The result would be the same if we made the opposite choice, so long as we were consistent.)
- When a pawn promotes, we denote that by following the move immediately by the type of piece promoted to, as in "b8Q", rather than "b8=Q" or "b8/Q". (Again, making a different choice would not change the result as long as we were consistent.)
- The English initials for pieces are used. (Yet another choice that would leave the answer unchanged, assuming consistency.)
- Captures ("x") and en passant captures ("e.p.") are recognized.
- Pawn captures must specify both the rank and file of the destination square, not just the file, even if a pawn is being captured. (Thus, we write "de5" rather than "de".)
- The initial coordinates of the moving piece are only given insofar as this is necessary to disambiguate the move (e.g. "Nge2"). Keep in mind that in some very rare cases, it may be necessary to include both rank and file for this purpose.
The Cluemeister thinks he's been able to work out how many moves are possible. Go ahead and take a stab at it! Feel free to take wild or educated guesses, as it's entirely possible no one will give the exact answer. If you show your work and address a point the Cluemeister missed, he'll take that into account—otherwise, the winner will be whoever's guess is closest to the figure he's come up with.
Send answers or questions to: thorin (dot) tatge (at) pobox (dot) com until December 29th.