Illegal Position Contest!

Oh. I thought you wanted a 72-move game with a total count of 144 plies. I should have realized you wanted something different.

I should, no doubt, have been more explicit.

Illegal. White's five pawn captures and capture of the c8 bishop exhaust White's captures. Before Black's last move, O-O-O+, the black pawns are in their final places. The h-pawn couldn't be at h6, or the white king couldn't reach g7. The a-pawn couldn't be at a7, or the black queen couldn't have gotten out to be captured by a white pawn.  If White last moved the king to g8, Black has no previous move. If White already had the king on g8 and last captured a black piece on g5 or h4, Black's only move would be castling, and one of the white knights would be left out of place.

Illegal. White has no legal retraction to uncheck the black king. Discovered check by a pawn capture on a3 would block the bishop's path to a1. Discovered check by a king move from c3 to b3 would require an en passant capture by Black on b3 to avoid an illegal double check, and again the bishop's path to a1 would be blocked.

Nice work! There were other tries in both positions. For example, in the position where black must uncastle, white could try to retract h6-h7, allowing black to retract h7xg6. But now white again cannot give a last move for black. As for the bishop check, I’m assuming you found other tries too obvious to be illegal.

Here’s #6509 with a few adjustments. Now is it illegal?

Correct! It is legal because of discovered rook check.

The above position is legal. But add ANY type of piece on g8 and the position becomes illegal. Why?

The white king has to go to h8 and the black king to f7 to let the white rook go to c7. When the white king has moved back to f7, g8 will be vacant and it will be Black's move, but no remaining black piece can ever move to g8. A black piece that tempos while a white knight moves to g8 can't be captured and will still be on the board.

Here's one way to get to the legal position.

Here's another way I just thought of to get to the legal position.

You haven’t mentioned about what happens if a white piece is added to g8. Then the last move must be the uncapture of a black unit on g8 (to give black a last move), but a black unit on g8 is illegal as you have stated. But again, well done!

Illegal because the rook could not have gotten there in the last move.

Illegal. To get the white king to h1, the f2 pawn moved forward and the h1 rook was captured. That leaves White with only five pieces to be captured, but the a7 pawn needs six captures on dark squares to promote on g1. The a2 pawn can only promote on a light square. The f2 pawn could make two captures to promote, except that Black is only missing one man. If the f7 pawn moved out of the way, it would need a second capture to return to the f-file. With the six captures by the a7 pawn and the capture of the a1 rook, that adds up to nine captures, but White is only missing eight men.

Note that this illegality proof works even if the black king is somewhere else, so that White has a last move of a piece to g1 to be captured.

Not quite, I’m afraid. Just because the a pawn promotes on a light square does not mean it must be captured on a light square (unless it promotes to bishop, but it can’t escape anyway). The king is on g5 for a specific reason, as I have a proof game for if he were anywhere else. Also the f pawn could capture fxe3 to get captured by the black pawn, or promote via fxg7 behind the black g pawn (but these are illegal for another reason!)

You're right. I must have been up too long when I worked out my proof.