Pandolfini's Puzzler #22 - Finding the Large in the Small

Pandolfini's Puzzler #22 - Finding the Large in the Small

brucepandolfini
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“Good morning, class,” the Professor bellowed out. “Are you ready to take another intellectual journey?”
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Zephyr and Lucian nodded “yes.” 
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“Well then, let’s begin. As you know, chess players have many talents. Some of these talents are generally known. Others are less well known. Can you tell me what talents you think chess players have?”
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“They can do things in their heads,” Lucian said confidently. “They can see the future.”
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“So can fortune tellers,” Zephyr joked.
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Everyone laughed.
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Lucian went on. “Aren’t they also supposed to have good memories?”
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“So does an idiot savant,” Zephyr jibed.
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Once again, the room was filled with chuckles.
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“That’s right,” the Professor continued. “But you might want to qualify that a bit.”
king dreaming white.png
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“I was kidding, but I do think I understand,” Zephyr illuminated. The public believes the good chess player has only a rote memory. But it’s more than that.”
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“Exactly,” the Professor resonated. “It’s not just about rote memory. It’s about having an active memory. Can either of you explain?”
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Lucian took a shot at it. “The good chess player can take something he’s memorized and use it to do something else. He can change what he’s memorized to help solve problems.”
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“Yes she can,” Zephyr interjected with a note of competition in her voice. “Her good memory is not just rote memory at all. She also has a working memory, just like the Professor said.”
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Everyone was still smiling and having a good time.
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“I think,” the Professor began, “you’re saying that good chess players look for analogies.”
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“What do you mean by analogies?” Lucian felt obliged to ask.
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“For now, I mean nothing more than this: they naturally make comparisons. Sometimes, that can mean finding the large in the small. Let’s see what I’m getting at. Consider our first position.”
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“It is White’s turn. White could be a he or she, it doesn’t matter. More importantly, White’s king is far away from the action, and Black’s king is close to it. Can White save the position?"
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That seemed like a tricky comment, so, for a few moments, the class looked over the position for snares. Then Lucian spoke up.
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“Professor, you showed us this idea before. The white king maneuvers in, is able to win the black e-pawn, and queen his own pawn. I think you called the idea outflanking or something.”
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“I remember,” Zephyr added. You said that White gets to the critical square, c6, and that leads to the gain of Black’s pawn. After capturing the pawn, White’s king is again sitting on a critical square.”
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“That’s right,” the Professor beamed back. “I’m very impressed with your memories and your reasoning. Obviously, the two of you are good chess players.” 
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The Professor continued: “That brings us to our second position. Maybe it will trigger your working memories and not just your rote memories.”
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Question: How can White play and force a winning position? 
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“Let me help you a bit more, not that your memories need much jogging.” Somewhat aphoristically, the Professor added: “See if you can see the future in the past.”
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As the class did, can you explain the analysis of both positions?
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Answers Below - Try to solve ProfessorPando's Puzzle first!
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ANSWER #22
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For diagram 1, White wins by starting with 1. Kb7.
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Black can now choose to defend or counterattack.
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Defending leads to something like this: 1…Ke7 2. Kc6 (occupying a critical outflanking square) 2…Ke8 (taking a meaningless diagonal opposition) 3.Kd6 Kf7 4. Kd7, and the e6-pawn falls.
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Counterattacking leads to something like this: 1…Kg6 2. Kc6 (occupying a critical square and taking a meaningful distant opposition) 2…Kf5 3. Kd6 (creating mutual zugzwang – neither player wants to move), and once again the e-pawn falls.
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For diagram 2, White can reduce to the previous solution by 1.Rb8+ Rf8 2. Rxa8! Rxa8 3. Kb7, and, very shortly, diagram 1 will wind up being diagram 2.
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Take note
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Among all the talents a good chess player tends to have is the ability to draw analogies between apparently different positions. For example, here is an imaginary dialogue that contains elements of the truth. Let’s pretend you’re looking at a particular position you need to analyze. “What should I be doing now? Does this position remind me of any I’ve seen before? Oh yes, it’s kind of like that, but not exactly. Didn’t he win that game? Hmm. Can I make this position look like that? What do I have to do to make that happen, or get to that winning setup?” And so it goes – the art of analogous thinking.

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