2025/03/21 DPA: "Underwhelmed But Overpowered"

White to move:

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Is there a checkmate possible if the pawn is on f7 and the Knight on g6?  The problem is that it will take too many moves and in the interim, Black can reposition his Bishop guard f7 and sac if the pawn moves.

1. f7 seems like a logical first move.  1. ... Bxe4  2. f8(=Q)#.

The Black King is frozen but Black has the drawing resource 1. ... Bg8:  if 2. fxg8(=Q)+ Kxg8  and it's a draw due to insufficient material; and if 2. f8(=Q), it's Stalemate because the Bishop is pinned and the King can't move.

Underpromoting to a Rook doesn't help as the Bishop is still pinned.

Underpromoting to a Knight doesn't help because White can't checkmate with 2 Knights in this scenario.

So underpromoting to a Bishop must be the answer:  if White can win the Black Bishop, he will have a K+B+N v K, a theoretical win [whether the Solver actually can execute it is not the point of the puzzle].

The light-squared Black Bishop can move anywhere and it won't matter because White's moves all involve dark squares:  3. Bg7+ Kg8  4. Nf6#.

Wait, that's not #:  4. ... Kf7.

Aah, so we rearrange the move order:  3. Nf6 Bishop moves  4. Bg7#.

Bingo!

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The keys were:

• The Black King's immobility meant we only had to calculate Bishop moves
• 1. f7 threatened promotion and checkmate so 1. ... Bg8 was forced
  • The Solver had to see the draw if either he captured or promoted to anything other than a Bishop
• 3. Nf6 closed the mating net [making sure not to jump the gun and play 3. Bg7+, which allows escape via f7]
• Recognizing that everything would happen on dark squares so Black's light-squared Bishop could not defend; not even deliver a check

The star Solver move was 2. f8(=B) but that was necessary to counter the ingenious defensive resource 1. ... Bg8.  This is a good example of not resigning to soon but too continue fighting on because you never know when you'll be given an opportunity to possibly draw.