2024/03/02 DPA: "Mating Net - 1 = Skewer"

White to move.

Black has back rank weaknesses.

If the Knight wasn't there, White could play 1. Qc8+ Qd8  2. Qxd8#.  So how can White move the Knight without losing tempo?

1. Nf6+ [Knight cannot be captured by the g pawn as it's pinned]:

• 1. ... Kh8  2. Qc8+ Qd8  3. Qxd8#
• 1. ... Rxf6  2. Qc8+ Qd8  3. Qxd8#
• 1. ... Kf8:  this neutralizes 2. Qc8+ since 2. ... Ke7 is possible.

Hmm, but maybe 2. Qc8+ Ke7  3. Nd5+ and the Queen and Knight form a great mating net.

3. ... Kd6  4. Qd8+ Ke5 and that isn't looking good.

1. Ne5 to prep allows Black time for 1. ... h6, which ends any back rank checkmate.

Note that Black's Rook is hanging but even if White wins it outright, is that sufficient?  He would have a Knight for 2 pawns but with Queens still on the board, that doesn't seem convincing.

So let's return to 1. Nf6+ Kf8  2. Qc8+ Ke7  3. Nd5+ [3. Ng8+ is also a check but it takes the Knight out of the action] Kd6.

With the Knight on d5, there is no chance for a Royal Fork since the Knight cannot attack the Queen on d2.

There might be a way to skewer the King to the Queen on the d file.

1. Qxf3 Qd7 would work if White could reach the back rank but he cannot.

There's no way for the Knight to move out of the way and guard f8 simultaneously.

After 2. ... Ke7, White's Knight is hanging.  The only Queen check is 3. Qxc7 but that allows 3. ... Kxf6 and I don't see any way of winning the Queen and certainly not checkmating.

So if White sacs the Knight, it must either lead to checkmate or winning the Queen.  Otherwise, it's a failed idea.

So at this point, I don't think White can afford to sac the Knight.

After 1. Nf6+ Kf8, besides the Queen check White can play either 2. Nxh7+ Ke7  3. Qe4+ [a great centralizing Queen move]...oh, but the King doesn't have to move to e7:  he could just move back to g8 and White hasn't gained anything except give Black luft [space].

Can White reorder the move sequence?  1. Nf6+ Kf8  2. Nd5.  However, this gives time for Black to play 2. ... g6, for example.

1. Nf6+ Kf8  2. Qc8+ Ke7  3. Ng8+ Ke6 [the King does not want to go to the d file because that allows the skewer 4. Qd8+ and White will win Black's Queen]...wait a minute:  3. ... Ke6 is not possible because of the Queen on c8.

I think that's it:  the Knight controls e7 and f6, the Queen controls the back rank, d7, & e6, and his own pawn blocks f7.  The only square for escape is 3. ... Kd6  4. Qd8+, winning the Queen.

Yup, that was it. 

Time:  50 minutes.

The challenging part was visualizing the mating net after 3. Ng8+:  since I can't do a blanket coverage calculation in my head, I have to do it one square at a time.  I typically start with the upper left square adjacent to the King and work clockwise.

• d8, e8, and f8 are covered by the Queen
• f7 is blocked by his own pawn
• f6 is blocked by the Knight
• e6 is blocked by the Queen
• d6 is open
• d7 is blocked by the Queen

Once I realized that d6 was the only open square [I initially did not "see" that], I knew I had the solution.

The key is that Ng8+ does not block the d file, allowing the skewer to work; Nd5+, while centralizing the Knight and therefore seemingly more logical, blocks the d file.