2024/03/23 DPA: "Boden + Knight = Checkmate"

White to move.

Black has limited King mobility.  In fact, if White could deliver check without disrupting the Bishops' control [ie Nb7 vs Nf7, which blocks the light-squared Bishop's control of e8], it would be checkmate.

White's c pawn is pinned and so cannot capture the Knight, which guards the e6 square that White would like to use [Nxe6 is also # but for the Black Knight on d4].

If the White Queen ever leaves the defense of the c pawn, Black will be able to take the offensive.

White cannot castle due to the Bishop's control of f1.

Obviously, the d6 Bishop should stay put since it controls c7 and e7.

Same goes for the g6 Bishop, which controls e8.

Black's Rook and d7 Knight complete the mating net by blocking the King's escape.

Oh, and ... Qa1+  Kf2 Qxh1 is also a threat.

The obvious first move is 1. Nf7+ as Black's response is forced 1. ... Ke8.

As soon as the Knight moves, the King will be in discovered check by the g6 Bishop.

Obviously, moving the Knight back to h8 accomplishes nothing.

2. Ng5^ [discovered check] allows the Knight to attack e6 but the Black Knight on d4 prevents this.  White could play 3. Qxd4 but that allows 3. ... Qxc3+  4. Qxc3 Rxc3 and the mating net is severed, although White has won a piece.

But that seems too simple, especially for a Saturday puzzle.

I see something:  1. Nf7+ Ke8  2. Nxh6^ Kd8  3. Qg5+ [made possible by the removal of the h pawn] but Black has 3. ... Nf6, which frees up the critical d7 escape.  I don't think White can allow either the Rook or the d7 Knight to move.

So that particular idea didn't work but it did show that Nxh6^ has utility.

Does White have time for a setup move somewhere in the sequence?  Kf2 I thought would escape all checks but that's wrong due to ... Qa2+.

1. Nf7+ Ke8  2. Qxe6+ Nxe6 doesn't accomplish anything.

No LQMs [Lateral Queen Moves] or BQMs [Backward Queen Moves] seem to help.

If White can get his Knight to e5, that could block the d7 escape but he has to discover a way to play Qg5+ without the Black g pawn to support Nf6.

We can do 2 out of the 3 things:  remove the h pawn to allow Qg5+ and get the Knight to e5 using 1. Nf7+ Ke8  2. Nxh6^ Kd8  3. Nf7+ Ke8  4. Ne5^ Kd8 but when White plays 5. Qg5+, Black has 5. ... Nf6.  And if White moves the Knight, Black can escape to d7.

This idea is worth pursuing, though, since it shows promise and because I can't find anything else.

I do see one winning line:  1. Qxd4 Qa1+  2. Kf2 Qxh1  3. Nf7+ Kf8  4. Nxh6^ Kd8  5. Nf7+ Ke8  6. Ne5^ Kd8  7. Qh4+ Nf6  8. Qh8+ Ne8  9. Qxe8#.

[edit:  this fails due to the Black Bishop on b5 which defends e8]

This is predicated on the assumption that Black goes for the Rook off in the corner rather than simplifying with 1. ... Qxc3+  2. Qxc3 Rxc3, where White wins a piece for a pawn.

The above line is elegant as it shows the Knight leaping back and forth, eliminating the h pawn which clears the h file for the eventual 8. Qh8+.  And it's very puzzle-like.

My intuition says that if Black choose the simplification line 1. ... Qxc3+, it's an edge for White but not much.

But the question is does White have anything that starts with 1. Nf7+?  And can White begin with 1. Nf7+ but at some point play Qxd4?  The problem appears to be that when White plays Qxd4 is arbitrary which means there is more than one solution [even though they are all related in move order].  This implies it's NOT the solution as there can be only one.

Aah, I see a problem with Qxd4:  ... Rc4, which stops Qh4+.

Also, practically speaking, a 9-move solution is a bit much, even for a Saturday.

I don't think I can win without some sort of setup move.  White's pain point appears to be ... Qa1+ which is also a double attack on the c pawn which allows ... Rxc3.

White cannot stop ... Qa1+ except with Qc1 and that move yields no advantage.

White can play Bb4, attacking the Queen and also defending the c pawn.  Black still has ... Qa1+ but after Kf2 Qb2+  Kg3, White is OK.

I've got it:  1. Nf7+ Ke8  2. Qxe6+ Nxe6  3. Ng5^ [discovered check] Kd8  4. Nxe6#.

Yup, that was it.

In hindsight, the key was the discovered check 3. Ng5^, which forced the King back to d8 but also attacked the Knight.

Where I went wrong was not more quickly recognizing that the final check would be delivered on e6.  I was thinking of how to get the Knight to b7, which could only happen if the Knight could double-hop from f7 to d6 to b7, which is impossible as long as the Bishop is on d6 and if White moves the Bishop, he loses control over either c7 or e7.