5/14/2025 DPA

Here's what we can note about this puzzle:

1. Blacks king is on back rank protected by a bishop

2. Our rook is blocked from moving to the back rank by our bishop

3. We are down a knight

First, we can offer an equal trade of pieces with Bxb6, but if black doesn't accept the trade, we are in a losing position. Even if black accepts the trade though, we have a draw by reputation.

So, neither the accepted nor unaccepted versions of Bxb6 works. What about 1. Bh6? After 1.... Bxh6 2. Qxh6 Rb1... Now the move we needed to play (3. Re8) doesn't work, as our rook is now pinned to our king.

OK, what if we try to move a different piece? Maybe we could play Rd1, preparing to move our rook to d8? If we play this move though, black can block our check early by playing Bf8. Any other rook moves either end in our rook being captured or black preparing a checkmate.

So we only have one more piece left, our queen (I'm not going to go into every pawn or king move, short version - they do nothing). What if we try to check? We can check blacks king by playing Qd8+. Black is forced to block with their bishop, and after Bh6, we're threatening mate-in-1... Except black has a mate plan of their own.

Alright, so every move after Qd8 has to be a check, but we only have one check in this position, surely sacrificing our queen won't give us anything, right? Well, after Qxf8, blacks king is forced to take back, NOW we can play Bh6+ (third times a charm, right?). Black is forced to g8, as moving our bishop opened up the e-file to block blacks king. And from this position, we can play Re8#.