Pandolfini's Puzzler #34 - Around the Chessboard
Professor: Hey, class, welcome to our circle of chess friends.
Zephyr: Welcome to you as well, Professor.
Lucian: We’re happy to arc across your day.
Professor: And I’m pleased to hear that I’m surrounded by such good cheer.
Lucian: They say good minds think alike.
Zephyr: Who’s “they”?
Professor: Perhaps you’re alluding to people from around the world.
Lucian: How about chess positions from around the world?
Zephyr: I’ll settle for chess positions from around the chessboard.
Lucian: That sounds rather circuitous to me.
Zephyr: I can be as circuitous as you can be circumloquacious.
Professor: Instead of pursuing that line of circumambient reasoning to its illogical conclusion, how about we segue into today’s position?
Question 1: How can White force mate in two moves?
Professor: Now, this is not a very hard position to win, with the black king encircled by hostile forces. Even so, it’s wonderful when you can checkmate the opposing king near the center of the board, which could have a certain aesthetic to it.
Lucian: I don’t know how beautiful it all is. But I do think I have a winning idea.
Zephyr: I think I have a winning idea as well.
And so they did. The two whizzes quickly had the correct answer, which made the Professor immensely proud.
Professor: Your quick and correct response pleases me greatly.
Zephyr and Lucian: Thank you, Professor.
Professor: But you know, the trajectory of this talk has made me a little dizzy. I don’t think I meant to show you that first position. I think I meant to show a slightly different position. Let me show you that slightly different position now.
Zephyr: You’re not thinking of sending us about in circles, around the chessic galaxy, are you?
Lucian: I hope the answer doesn’t lie at Star’s End.
Professor: Let’s leave Isaac Asimov out of this and just go to the next position.
Professor: Clearly, this position's key structure is essentially the same as the first position. Can you find the mate in two?
Question 2: How can White force mate in two moves?
Once again, the Professor’s chess SWAT team went to work. After five minutes (if it took that long), the crack unit of Zephyr and Lucian had the answer.
Zephyr: I suppose that shifting forces to the next quartern has some humor to it, Professor.
Lucian: I’m laughing, less at the change of position and more at the choice of words.
Professor: Well, if you didn’t mind the 90 degree shift in focus, I suppose we can do it again.
Zephyr: Uh, oh. Here comes a third position.
Lucian: I bet it’s even related to the first two.
Question 3: How can White force mate in two moves?
Professor: To me, it’s the same position, but trivial differences can make all the difference.
Lucian: I’m getting a tiny bit tired of turning my body around so.
Zephyr: It‘s more exercise than some chess players get in an hour.
Professor: Instead of physically exercising, I’m more interested in exercising the mind.
Zephyr: I’m more interested in exorcising this problem. After getting rid of it, maybe we could play some chess.
So the task force got their minds together and worked out the answer. And the Professor was pleased – so pleased, he had to offer one more example.
Question 4: How can White force mate in three moves?
Professor: I know the differences are quadrivial, but moving our thoughts to the next quadrant has moved me deeply. The only thing is now it’s not mate in two. It’s mate in three, so we’re back to the trivial.
Lucian: If solving this last problem means we can play some chess, I’m all in favor of it.
Zephyr: But Lucian, we’ve already solved most of it. Haven’t we?
Can you solve all four problems? And what did Zephyr mean by saying they had already solved most of it?
Lucian: Chess anyone?
Answer below - Try to solve ProfessorPando's Puzzle first!
For problem 1, the answer is 1. Qh7! Ke5 2. Qe4 mate.
For problem 2, the answer is 1. Qb6. If 1…Ke4, then 2. Qd4 is mate; or if 1…Kc4, then 2. Qd4 is still mate.
For problem 3, the answer begins with 1. Qb3!. If Black then tries 1…Kd6, White plays 2. Qd5 mate. And if Black instead tries 1…Kd4, White still plays 2. Qd5 mate.
Finally, for problem 4, the answer begins with 1. Bb2!. What Zephyr and Lucian realized is that the mate-in-three is the root idea for the other three mates-in-two.
After 1. Bb2!, here’s the summary of winning variations:
If 1…Kc5, then 2. Qb8 and mate next.
If 1…Ke6, then 2. Qc7 and mate next.
If 1…Ke4, then Qg3 and mate next.
Two terms often used in chess compositions are rotation and reflection. A rotation essentially refers to the same exact setup among and between the pieces, but in a different quadrant of the board.
The problems above do not represent true rotations, since the positions, from diagram to diagram, are a little different, at least because of the placement of the black king. A reflection has to do, not with the same setup, but with a comparable or opposite one, as if being perceived in a mirror.