2025/06/06 DPA: "No Mate, No Sac, No Problem!"

Black to move:

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1. ... Qh2+  2. Kf1 Qh1  3. Ng1 and how does Black proceed?

Material is equal.  Black's Knight is hanging and White also threatens to win the Bishop with 2. Qxd6 Bxd6  3. Rxd6.

If Black could play ... Qxa4, it would remove the Queen from attack, win the Knight, AND protect his own Knight.  Then again, the Knight is trapped so what could Black do after Rb1, adding a second attacker?

Moving the Queen backwards doesn't do anything other than either lose the Queen on d7 or the game on d8 [ie Qxd8+ Rxd8  Rxd8#].

1. ... Qh2+  2. Kf1 Qh1+ [2. ... Nd2+ just loses the Knight]  3. Ng1

1. ... Rc1 and now if 2. Qxd6 Rxd1+  3. Qxd1.  OK, that doesn't work.

I don't see any Rook move that holds promise.

No Bishop move.

1. ... Qh2+  2. Kf1 Qh1+  3. Ng1 Bh2  4. Ke2 Rc1 and now if 5. Rxc1 Nxc1+, a Royal Fork.

Ah but White will play 5. Qd8#.

What if we reverse the move order?  4. ... Nc1+  5. Rxc1 Rxc1  6. Qd8#.

I think I'm on the right track, though.

3. ... Bh2 is not a forcing move:  4. Qd8+ Rxd8  5. Rxd8#.

As soon as the Queen leaves protection of d8, White has the chance to play Qd8+, leading to checkmate.

I think the solution must also involve the Black Rook reaching the back rank but it must come with check due to White's threat of Qd8+.

1. ... Qxd3  2. Rxd3 is still safe for White since c1 is protected.

2. ... Qh1+ seems to be key in getting the White Knight off of e2 so it no longer guards c1.

3. Ng1 but Black's next move cannot be 3. ... Bh2.  It must be a check or something that blocks the d file [Black could also play 3. ... Rf8 but that accomplishes nothing].

1. ... Nc1  2. Qxd6 Nxe2+  3. Kf1 Bxd6 but now both of Black's pieces are en prise.

4. Kxe2 or Rxd6 evens things out.  No fork opportunities.

I think I see it:  1. ... Qxd3  2. Rxd3 Nc1, forking the Rook and Knight:

• If 3. Nxc1 Rxc1+  4. Rd1 Rxd1#
• If 3. Rd2 to protect the Knight, 3. ... Nxe2+  4. Rxe2 Rc1+  5. Re1 Rxe1#
• If 3. Kf1 to protect the Knight, 3. ... Nxd3
• If 3. Nb2 Nxd3, winning the exchange
• If 3. Rd1 Nxe2+

Yes, that was it.

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The first key was recognizing that no win existed starting with 1. ... Qh2+, which seems like the most obvious place to start.

Another key was seeing that no Queen sac [or Rook sac] yielded any results [some solvers like to complain about the Daily Puzzle *always* being about a Queen sac].

Then the final key was seeing the fork, not so easy because we usually don't think about a fork when one of the targets is a Knight, since it can capture our attacker.

This was a ZAS*, where the Queen exchange set up 2. ... Nc1, forking Rook and Knight:  If the Rook moves, we can either win the Knight or exchange Knights and then checkmate on the back rank.  If anything else, we win the exchange.

*Zombie Attack Scenario:  the opponent is trapped in a room with doors at both ends with no locks and Zombies are closing in.  The opponent can bar one door or the other but not both.

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Yes, the opponent play was not sub-optimal:  best was to accept the loss of the Knight and play on.  However, A) the game was still won for Black [-4 advantage]; and B) more importantly, the puzzle creator wanted to showcase the back rank tactic, which would not be possible if the opponent had played optimally.

This is a common occurrence in puzzles and one that frustrates, surprises, and vexes the solvers who believe, mistakenly, that the opponent *must* make all optimal moves.  Once they accept that opponent sub-optimals are allowed, even encouraged, they'll be a lot happier.

Those that refuse to accept this will continue to be frustrated.  Their choice.

Nice puzzle, @chesstiger787!