Pandolfini's Puzzler #63: Two Knights In Shining Armor

Professor: Hello, Class. 

Class: Hello, Professor.

The class resounded as one, but very low.

Professor: Rachel, you wanted to show us a position?

Rachel: Nothing special. It came from the club ladder.

Professor: Wherever it came from, let’s see it.

Rachel went up to the demo board and set up the following position.

Question 1: How does White force mate in 2 moves?

Thomas:  Oh, that was your game against Gandelbrot.

Lucian: Did he resign after you played your move?

Rachel: He knocked over his king and stormed off.

Thomas: That’s Gandelbrot!

Zephyr: I suspect he didn’t like those two knights.

Hale: If only Black didn’t have a bishop.

Ryan: Then the position would be drawn.

Idris: Unless there’s a mate already set up in the position.

Ryan: Or if Black had a pawn move, there’d be no stalemate.

Professor: Interesting. Let’s consider another two-knight position.

Question 2: How does White force mate in 2 moves?

Finding the answer to this one pretty quickly, the class spent the rest of its energy trading a few jibes.

Hale: It’s a kind of zugzwang.  

Lucian: Yes, but defender is so defenseless. Suppose you add stuff?

Professor: Fine. Let’s add a knight.

Question 3: How does White force mate in 2 moves?

The problem was solved instantly (by Zephyr, according to Zephyr), but it was hard to say who got the right idea first.

Lucian: Problem 2 is like Problem 3. 

Zephyr: No, it’s more like Problem 3 is like Problem 2.

Hale: That’s zugzwang?

Idris: It’s not a true zugzwang, since it’s not reciprocal.

Zephyr: I had a premonition you’d say that.

Lucian: Professor, can you add more material than that?

Professor: Sure. Let Black be up by a double Exchange.

Zephyr: Something tells me White is going to win anyway.

Question 4: How does White force mate in 3 moves?

A minute is all the group needed. The only question centered on which knight to move first. 

Rachel: Let’s hear it for well-placed knights!

Zephyr: And poorly placed defending rooks!

Hale: We know about the advantage of two bishops, but the advantage of two knights?

Ryan: Generally, I don’t think so.

Thomas: May we see another position, please?

Professor: Okay, this time, Black has connected passed pawns on the 7^th rank.

Zephyr: Gee, thanks!

Question 5: How does White force mate in 3 moves?

The class stalled for a moment over the winning idea. Connected passed pawns on the seventh rank can do that to you. But the winning line was found, by Ryan and Idris, and the discontinuous discussion discontinued.

Lucian: Admittedly, I had to look twice at that one.

Zephyr: Are you sure it wasn’t three times?

Professor: I’m only sure that the next problem is our last for the day.

Question 6: How does White force mate in 3 moves?

The general idea was worked out smoothly enough, the main caution being the possible discovered check along the h-file. But the class got around that just fine 

Lucian: So what can we say about all of this?

Zephyr: What do you want us to say?

Lucian: Anything, as long as you’re not the one to say it.

As the class filed out of the room, even Zephyr had to smile.

Answers below. Try to solve NM Pandolfini's puzzles first!

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Answer 1: Black is helpless after 1. Kh3. He can guard f2 or g3, but not both, and so the e4-knight mates next move.

Answer 2: White wins with 1. Nc6!, and there’s no way to stop a mating knight check from c3.

Answer 3: The killer move is 1. Kh8!

If the e7-knight moves, White’s f4-knight mates on g6.

If the c5-knight moves, White’s f4-knight mates on e6.

Answer 4: White mates in three moves by 1. Ndf6+ Kf8  2. Nh7+ Ke8  3. Nhf6 mate. 

Answer 5: The winning line is 1. Nd3+ Kd1  2. Kb1! e1/Q  (or any other promotion) 3. Nb2 mate.

Answer 6: The forced winning variation is 1. Nh6+ Kg7  2. Nf5+ Kg8  3. Nxe7+ Kg7  4. Nf5+ Kg8  5. Kg4! Nf8  6. Nxf6 mate.

Starting from most natural positions, king and two knights cannot beat a lone king. The main difficulty is that one move before issuing mate the attacker would effect stalemate. That’s why, where feasible, the attacker tries to allow the defender to keep an extra pawn.

That way, stalemate is avoided by the defender being able to make a pawn move, even sometimes promoting the pawn in the process. But, obviously, this can be quite problematic. Various endgame texts deal adequately with such two-knight vs. pawn positions. A good presentation, for example, can be found in “Batsford Chess Endings,” by Speelman, Tisdall, and Wade (pages 112-115).

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