Well, hi everybody. I've got kind of a problem I really would appreciate help with. As I am Swiss, some of my expressions might be unusual and I would ask you for your understanding and forgiveness.

Thank you.

So yeah, how the heck would I go about solving that problem?

In a 8x8 sized chessboard, both black and white play with 16 pieces each, which limits the pieces on board to 32.

Each colour's pieces consist of:

- 8 pawns
- 2 rooks
- 2 bishops
- 2 knights
- a queen
- a king

How many different (and possible) positions exist?

Take into account that:

- The white pawns cannot reach the first rank and likewise, the black pawns cannot reach the eight rank.
- A bishop can only move on half of the squares, either white or black ones (one of each colour moves but on white squares, the other on black squares only).
- White pawns that reach the eight rank and black pawns that reach the first rank can be promoted to either a rook, knight, bishop or queen of the respective colour, independently of the pieces taken prior to the promotion.
- Pawns may only change the file they move in by taking pieces.
- A pawn cannot reach the opposing rank (8 for white, 1 for black) if the opponent's pawn in the file it's moving in is not taken.
- The two kings must not stand next to each other.
- During play, all pieces except for the two kings may be taken.

It would have been fairly easy if it were but "32 pieces on a 8x8 board", methinks, but all those "take-into-considerations" really get the best of me.

Can somebody help me? If you can indeed, it is appreciated if you do too.

Thanks in advance.