If one of the following is true, a position is not reachable from the starting position by a series of legal moves:
- One side has two or more kings or one side has no kings;
- One side has a total of 10 or more queens and pawns, or a total of 11 or more rooks and pawns, or a total of 11 or more knights and pawns, or a total of 10 or more bishops of the same colour and pawns;
- One side has a total number of more than 16 pieces;
- At least one pawn is in the first rank or eighth rank;
- Both kings are being checked;
- The kings can capture each other in the next move;
- At least one bishop is in an "impossible square" blocked by pawns in their starting positions, such as the following:
- One king is being "impossibly" checked or checkmated such as the following (this should also include the case where a king is being checked by three or more pieces): (I am not sure how to define this more precisely);
- One side is checking and it is his turn.
I am sure that this list is not exhaustive. Does one know a complete list? Is there an algorithm determing whether a position is reachable from the starting position by a series of legal moves?
Edit: I would also add the following:
- One side has more than 8 pawns.