2025/05/25 DPA: "When One Door Closes, Another Opens"

Black to move:

.

Black is down the exchange.
White's King is immobilized but the back rank is protected.

1. ... Nf2+  2. Rxf2
1. ... Ng3+  2. hxg3 gxf4 [threatening 3. ... Qh5#]  3. g4 Qxg4. 4. g3:  once White can play g3, Black's checkmate disappears, as any check along the h file can be met with Kg2.

Maybe we can re-order:  1. ... Ng3+  2. hxg3 Qg4 [threatening 3. ...Qh5#]  3. Be2 Qxg3 [threatening 4. ... Qh4#]  4. Bg4 [intending to block 4. ... Qh4+ with 5. Bh3] Qxe1+  5. Kh2 Bg1+. 6. Kh3 Qh4#.

Plenty can go wrong in a 6 move sequence so let's look for any moves whose response is not forced.

    •    2. hxg3 is forced, as White can't block check nor move
    •    3. Be2 is the only move that contests 3. ... Qh5#
    •    4. Bg4 is the only move that guards against 4. ... Qh4#
    •    5. Kh2 is forced
    •    6. Kh3 is forced

That appears to be it.

No, that's wrong:

- The BQM [Backward Queen Move] 2. ... Qg6, which threatens an h file checkmate

- 3. ... g4 blocks the Bishop's access to h3, which could block the check

- 4. ... hxg6 opens up the h file for the Rook and checkmate is unstoppable

My failure was  not seeing 4. Bf5 but only considering Be2, which doesn't even lead to  checkmate since 4. ... Qxg3 could be met with 5. Ra3 [although still winning for Black].  Had I seen White's refutation of 2. ... Qg4, it's an open question whether I would have seen 2. ... Qg6.

Had White made the moves I visualized, my checkmate sequence was accurate but those 2 mistakes obviously foiled my attempt.

Nice puzzle by @JohanVA, our resident MPC [Master Puzzle Creator].