10 Dec '02 21:32

Just for my own curiousity (and because this sort of came up in

another thread,) I was wondering if we could figure out a formula to

calculate the total number of possible legal positions on a

chessboard. There are a bunch of criteria to consider, so here are the

ones that I was able to come up with:

A chessboard has 64 squares, 32 black and 32 white.

Both sides must have a king.

Neither side can have more than 8 pawns.

The sum of the number of queens, knights, rooks, bishops and pawns

cannot exceed 15 for either side (think pawn promotion.)

White cannot have any pawns on rank 1, black cannot have any on

rank 8.

Other criteria are more complex: I can't imagine any possible play

resulting in, for example, eight white pawns on rank 5 and eight black

pawns on rank 4.

Can anyone think of more that I've missed? Or derive a general

formula including these (and any additional) criteria that can calculate

the total number of positions?

-mike

another thread,) I was wondering if we could figure out a formula to

calculate the total number of possible legal positions on a

chessboard. There are a bunch of criteria to consider, so here are the

ones that I was able to come up with:

A chessboard has 64 squares, 32 black and 32 white.

Both sides must have a king.

Neither side can have more than 8 pawns.

The sum of the number of queens, knights, rooks, bishops and pawns

cannot exceed 15 for either side (think pawn promotion.)

White cannot have any pawns on rank 1, black cannot have any on

rank 8.

Other criteria are more complex: I can't imagine any possible play

resulting in, for example, eight white pawns on rank 5 and eight black

pawns on rank 4.

Can anyone think of more that I've missed? Or derive a general

formula including these (and any additional) criteria that can calculate

the total number of positions?

-mike