Originally posted by SwissGambit
[fen] 8/1k6/8/8/8/5B1B/7B/K4BB1 [/fen]
This position is legal - white's last move was Bd1-f3# or some such. Before that, bK wandered along the long diagonal while the other Bishops took their places.
In your 2nd diagram, we can replace a pawn with a King to make it legal.
[fen]8/2K5/8/4kPP1/2P2PP1/2P2PP1/8/8 b - - 0 1[/fen]
Hey SG,
adding the king helps, but there is another problem: the mating pawn move couldn't have occured, because the square it came from is occupied by another pawn. So at least the f4-pawn has to be replaced by a d4-pawn. Then, the last move was d3-d4# (or d2-d4# ).
Number of legal essential 9-piece checkmate patterns with only king and pawns (relative to defending king square) = 4*1*2*2 = 16
Starting from the original 9-pawn mate set-up:
- the king should replace 1 of the 4 pawns covering the corner squares. Replacing other pawns makes other pawns redundant or is illegal. So the king could be on c7, g7, c3 or g3.
- the c and g pawns (or replaced by a king) are fixed. These cover d and f files, which if covered with e-pawns would lead to redundancy.
- there are 2 possibilities for the mating pawn (covering e5), i.e. d4 and f4 --> this dictates the position of the pawn covering e4 (so 2 combinations d4+f3 and d3+f4)
- there are 2 independent possibilites for the pawn covering e6 (d5+f5)
I'm just wasting time.