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# Pandolfini's Puzzler #15 - The Circle Game

| 16 | Scholastics

“Life can be funny,” the Professor began. “There are times when it seems we go round and round, never getting anywhere special.”
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“That sounds very philosophical,” Zephyr offered. “The other day my math teacher mentioned Euclid and about how important the circle is in his principles of geometry. Is the circle also important in chess?”
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“No, I wouldn’t say so,” the Professor said. “Not especially,” the Professor went on.
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Lucian had to interject his own comment, just to keep it balanced.
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“Important or not, I sense you’re about to wheel in the next problem,” Lucian said.
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Proud of his play on words, Lucian continued: “If you are, Zephyr and I are ready and able.”
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It was clear that Lucian was feeling more and more comfortable working with Zephyr as a team and he wanted Zephyr and the Professor to know it.
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“Yes, you may have something there, Lucian,” said the Professor. “I have been taking you on a kind of merry-go-round, aiming to introduce the next problem. But before we go linear, first look at the following position.”
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White to move:
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Question: Can White force mate in four moves?
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“Obviously, you can mate without trouble having such a material advantage,” the Professor added. “But I want to know if you can do it in four moves.”
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The Professor tendered one more thought: “Are you prepared to encircle your imaginary opponent one more time?”
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Zephyr and Lucian smiled at each other. They could tell a professorial clue when they heard one. So they began to think out and mentally try variations, conveying their thoughts to each other in chess notation.
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After a bit, Zephyr was the first to speak, and she smiled as if it were a joke.
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“I can see that the rook can’t stay along the 4th rank,” she amusingly offered.
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“Oh, of course,” Lucian shot back, not seeing her attempt at humor. “That would be stalemate.”
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Meanwhile, Zephyr noticed that the Professor kept looking at the big wall clock. To her way of thinking, since it wasn’t time for the session to end, it had to mean something.
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Lucian noticed it, too. Then, it was as if an alarm went off. All excited, he whispered something to Zephyr, and the two of them appeared to analyze a particular variation.
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After a minute or two, they confidently let it be known that they had the answer.
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“We have it,” Zephyr spoke up for the both of them.
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Lucian nodded agreement.
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However, under his breath he muttered: “I can think as quickly as you can. I just can’t speak up as fast.”
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What variation had Zephyr and Lucian analyzed correctly (together)?
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Also, how did the answer fit in with the Professor’s puns and funny talk about circles?
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Answers below - Try to solve Professor Pando's puzzle first!
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The winning variation the two analysts found was: 1. Kd1 Kf2 (forced)  2. Kd2 Kf1 (the only move) 3. Ke3 Ke1 (again forced) 4. Rg1 mate!
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The circle clues, and the Professor’s staring at the clock, had to do with the way the kings move around the pawn in a clockwise fashion. In the end, the two kings have traded places.
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Take note
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The lines on the chessboard, and the patterns pieces trace, can be very beautiful. And memorable! Indeed, one way to increase your visualization, as well as your strategic thinking, is to take a diagrammed position and draw lines and vectors to where you’d like the pieces to go. In a way, it’s somewhat like sketching a football play, with you as the coach planning it out and with you as the quarterback calling the signals.

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