White to

This is the hardest endgame study you will ever see.

Bxg2

what about a draw with a different move

as Bxg2 leads to an endgame a rook and pawn down

White's complete set of legal moves:

you've still missed it

It's not a legal move anymore and It hasn't been for a while

Promoting to a king doesn't help, since the other is still mate. Promoting to a black piece doesn't help either.

Maybe promoting to a rook and castling (if the king started on g2)?

1. bxa1=R 2. gxh2 O-O-√O-O - to move 2 squares towards the rook, the king would have to move 12/√85 squares to the left and 14/√85 squares up, and since the black pieces are stuck on integer coordinates, they can't threaten the white king...

I'll give you a hint. The pawn reaches the 8th rank

If the pawn reaches the 8th rank but doesn't promote, white is still mate. If the pawn reaches the 8th rank and keeps moving, it could continue to the 9th rank and cause a buffer overflow, possibly resulting in a draw (or it could result in purple winning).

1. Kxg3 Bxg3

My guess. I'm assuming that because the bishop's there.

I also played monster chess with someone where the king can move twice, so it'd be like,

1. Kxg2-xg3    - in this case.

ex:

King starts on f2; Ke1-d1 in one move.

Because you say it's not legal "anymore" it means you're looking for an en passant or a castle -- casteling queenside by moveing the king to c1, regardless of moving through check and there's no rook wouldn't work anyway.

En passants land on the 6th rank so there are none there that were even legal a long time ago especially not one involving capturing c7 and none that would help anyway.

If you're going to allow illegal moves though, why not white to win:

bxa8, promote to a pawn. This was once a legal move but not anymore. Too bad, I've seen this puzzle before. :P No other move prevents gxh3 followed by h2# (promoting to a pawn prevents this because gxh3 is now stalemate).

I didn't know it used to be legal to choose not to promote and leave it a pawn, that's interesting.

correct tyzebug. Steinitz declared the pawn should be able to stay a pawn because of positions like that where staying a pawn stalemates yourself. here's a new puzzle with a new Illegal move which once was legal.

This one is clever. I've seen something like it before, I'll just let others figure it out, though.

does white promote to a black knight?

Not sure, is it b8=BlackN

yup white promotes to black knight. The rules once were The pawn had to promote. Then It was had to promote to a piece of the same color. Next it was it can promote but didn't have to and  it had to stay the same color. Finally it is today like the old rule that it has to promote, and has to stay the same piece

ok here is a puzzle you cant solve