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# Pandolfini's Puzzler #32 - Seeing the Large in the Small

Mar 7, 2014, 12:00 AM 12 Scholastics

Professor: Hello, Class. I hope you’re having a wonderful day.

Zephyr & Lucian: Thank you, Professor. We hope you’re having a wonderful day, too.

Professor: I am, especially now that I’m wearing my new jacket with its checkerboard design.

Lucian: Checkerboard? Don’t you mean chessboard?

Zephyr: Oh Lucian, both chess and checkers use the same board. You know that.

Professor: How true. But more importantly, do you like my jacket’s checkered chessboard pattern?

Zephyr: How could we not? It’s so dapper.

Lucian: How could we? It’s too dapper. And I can say that, never having used the word sartorial in polite thought.

Zephyr: Very funny. Well, somewhat funny.

Professor: You know, this three-way banter reminds me of a position. It’s not a hard position, but there’s a three-ness to the position that smacks of a chess triangle.

Question 1: In the position of diagram 1, can White force a win?

Professor: The situation offers White two virtues. White has an extra pawn. It’s also White’s turn to move, assuming that’s a virtue.

Lucian: If White plays 1. Kd6, Black has 1…Kd8, taking the opposition, when 2. c7+? only draws.

Zephyr: That seems pretty clear, Lucian.

Professor: What about if, instead of 1. Kd6, White tries 1. Kc5? Does that work any better?

Lucian: Not really, Professor.

Zephyr: Black replies 1…Kc7 and the white king still can’t get in.

Professor: Just a thought, class. We see that direct tries seem to go nowhere. What happens if it’s Black’s move to start?

Zephyr: Well that’s another story altogether.

Lucian: Sure thing. If Black goes first, and plays 1…Kd8, then it’s White who takes the opposition with 2. Kd6, and the c-pawn will soon queen.

Zephyr: And if Black instead tries the first move, 1…Kc7, then White plays 2. Kc5 and the white king moves into b6 next.

Professor: So are you suggesting that the winning idea is to create the same position, but with Black to move?

Lucian: I guess that’s what we’re suggesting, Professor.

Zephyr: Thanks for helping us put our thoughts into words.

Professor: My pleasure. Let’s move the triangle along. I’d love to hear specifically how you think White can win.

A little puzzled by the Professor’s remarks, the two students extraordinaire began to analyze. They quickly found a winning variation. In fact, they found two winning variations. That is, Lucian found one, and Zephyr found another. The two of them even understood what the Professor’s three-way talk was all about.

Professor: That’s wonderful, and I especially like the explanations you gave for your perambulation, or whatever you called it. But you know what? All of this reminds me of another position.

Zephyr: Oh Professor!

Lucian: Another position?

Professor: Why not? This way we can show “the other,” well, that is, another side to the triad. And I promise not to say anything about Hegel.

Lucian: Hegel?

Professor: How about we just take a look at the position?

Question 2: Can White force a quick win from the position of diagram 2?

Lucian: I know I’ve seen this position before. If it’s Black’s turn, I think he loses in five moves or less.

Zephyr: Yes, she either drops the rook or gets mated.

Professor: Wow, I see we have a little thesis/antithesis going on. To be sure, I’d love to hear about your synthesized answer. It should make everything absolute and clear.

---

Lucian: Can you clear it up a trace more and tell us exactly what we have to do, Professor?

Zephyr: This time in English?

The Professor explained everything, and the Whiz Kids went to work.

Overall, here’s what they had to do.

A) Answer question 1, showing that it is a win with White to move, making sure to give the two correct variations, Zephyr’s and Lucian’s.

B) Then show from diagram 2 that, by going first, Black loses the rook or gets mated in several moves, with sample variations for each first move for Black.

C) Then, for diagram 2, if it’s White’s move, show how White can achieve the same setup with Black to move.

D) Finally, explain how diagrams 1 and 2 are related in the Professor’s way of thinking.

Answers below - Try to solve Professor Pando's puzzle first!

A) For diagram 1, there are two variations that immediately work.

Zephyr found 1. Kd4! Kd8 2. Kc4! Kc8 3. Kd5, creating the same setup but with Black to move. Zephyr called the maneuver of the white king triangulation.

Lucian found a similar idea, but he started with the move 1. Kc4!. After 1…Kd8, the variation continues 2. Kd4! Kc8 3. Kd5.Lucian called his king maneuvertriangulation also.

B) For diagram 2, if Black goes first, here are sample variations for all tries:

If 1…Kh6, then 2. Qf8 soon mates.

If 1…Rg6+, then 2. Qxg6+ mates next move.

If 1…Rf7+, then 2. Qxf7+ mates next move.

If 1…Rg8, then 2. Qh5 is mate.

If 1…Rg4, then 2. Qh5+ wins the rook.

If 1…Rg2, the centralizing queen check, 2. Qe4+, wins the rook.

Both 1…Rd7 and 1…Re7 hang the rook.

If 1…Rb7, then the centralizing queen check, 2. Qe4+, wins the rook.

That leaves 1…Ra7, 1…Rc7, 1…Rg3, and 1..Rg1.

For 1…Ra7, the key connection point is g1. A sample winning line is 2. Qe4+ (a centralizing queen check) 2…Kg8 3. Qd5+ Kh8 (3…Kf8 allows 4. Qd8 mate) 4. Qh1+ Kg8 (on 4…Rh7 White has 5. Qa8 mate) 5. Qg1+, winning the rook.

For 1…Rc7, the key connection point is h2. A sample winning line is 2. Qe4+ (a centralizing queen check) 2…Kg8 (2…Kh6 is met by immediate mate) 3. Qg2+ Kh8 (or 3…Kc8 4. Qa8+; or 3…Kh7 4. Qh2+, forking king and rook) 4. Qh2+ Rh7 5. Qb8 mate.

For 1…Rg3, the key connection point is h4. A sample winning line is 2. Qe4+ (a centralizing queen check) 2…Kg8 (of the king stays on the h-file, the rook is lost to 3. Qh4+) 3. Qc4+, and either Black gets mated or drops the rook next move.

For 1…Rg1, the key connection point is a7. A sample winning line is 2. Qe4+ (a centralizing queen check) 2…Kh8 (2…Kg8 is no better) 3. Qa8+ Kh7 (3…Rg8 4. Qh1 mate) 4. Qa7+, occupying a connection point, forking king and rook.

C) If White goes first in diagram 2, the same setup, with Black to move, can be achieved by 1. Qe4+ (a centralizing queen check). If 1…Kh8 (or 1…Kg8), White has 2. Qa8+ Kh7 3. Qe8, and the white queen has triangulated to make it be Black’s move from the starting position! Note that 1. Qe4+ Kh8 2. Qa8+ Rg8 3. Qh1 is mate. From the beautiful center square e4, the white queen operates in all directions.

D) In the Professor’s way of thinking, the maneuvering pieces (for diagram 1, the king; for diagram 2, the queen) trace a triangle in their movements to make it the other player’s move. Thus, for diagram 1, the white king traces a triangle by going Kd5-d4-c4-d5 or Kd5-c4-d4-d5. For diagram 2, it’s the white queen that traces a triangle, going Qe8-e4-a8-e8. To the Professor, it’s seeing the large in the small.

Take note

In the variations above, a key theme is the importance of queen centralization. In the beginning of a chess game, it’s hard to establish a queen in the center, since there are usually useful ways the opponent can attack a queen and drive it from the center.

Indeed, bringing out the queen too early, without concrete purpose or necessity, can lead to loss of time, if not loss of the queen itself. But later on, posting a queen in the center can be a great advantage, since a queen in the center radiates in all directions. To be sure, a primary principle in queen endings is to place your queen in the center, to increase her possibilities while limiting the scope of “the other.”

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