# Pandolfini's Puzzler #42 - Trivial or Quadrivial?

• NM brucepandolfini
• | May 16, 2014
• | 4945 views
• | 20 comments

Professor: Welcome, class. Are you ready for some chess?

Class: Yes we are, Professor.

Professor: I thought today we’d take it easy and look at a few trouble-free problems, nothing special. With various tournaments coming up, it can’t hurt to stay sharp.

Hale: What kinds of problems, Professor?

Professor: Oh, simple tactics.

Lucian: What kinds of simple tactics?

Professor: Oh, uncomplicated ones. Maybe nothing more than rooks and knights at play.

Ryan: OK. I’m ready. Show us what you have.

Professor: Well, let’s start with this undemanding miniature and go from here.

Question 1: What is White’s best move?

Hale: That’s ridiculously simple. Although I do like the final position, as simple as it is.

Zephyr: Let’s see another plain one.

Professor: OK. You’ve asked for it. White mates in two moves, but there are two ways to do it.

Question 2: What are White’s two best moves?

Ryan: One of them is easy. In fact, it’s really primitive.

Lucian: You mean like ancient? Or do you mean like for Neanderthals?

Hale: I don’t mean whatever you just said. Besides, Neanderthals were actually pretty smart.

Zephyr: Yes, but very few of them could play chess.

Professor: Well, let’s see if your evolved status can help you solve this next one.

Question 3: What is White’s best move?

Lucian: You must be kidding, Professor. This, too, is so unsophisticated.

Hale: I agree with Lucian, and I don’t always agree with Lucian.

Zephyr: I agree with Hale, and I don’t always agree with Hale.

Professor: All right, I’ll tell you what. I also feel like being agreeable. Let’s take away Black's rook and knight and make it even less convoluted.

Question 4: Can White stop Black’s pawn?

Zephyr: You know, Professor, this may look slightly more complex, but it’s just as trivial as the other three problems.

Professor: Is it that trivial?

Ryan: No, it’s not that trivial. I’d say it’s more quadrivial.

Answer below - Try to solve ProfessorPando's Puzzle first!

For diagram 1, the answer is 1. Rd5+! Nxd5 2. Nc6 mate.

In diagram 2, there are two mates in two. Ryan found 1. Rh7+ Nxh7 2. Nf7 mate. And Zephyr found 1. Nf5+ gxf5 2. Rf6 mate.

In diagram 3 White wins with 1. Kb2!, creating a kind of zugzwang. Since Black can’t move the knight without allowing 2. Rb8 mate, he must drop the Exchange by 1…Ra7. After 2. Nxa7, White should win from there.

In the 4th diagram, White saves the day with 1. Nb5!. Assuming Black promotes, 1…c1/Q+, White has 2. Nc3+. Two variations then lead to a quick victory for White:

If 2…Qxc3, then 3. Kxc3 Ka3 4. Ra5 mate.

And if 2…Ka3 instead, then 3. Ra5+ Kb2 4. Ra2 mate also does the trick.

Take note

A terrific cache of rook and knight vs. rook and knight endgame shots can be found in Van Perlo’s “Endgame Tactics: A Comprehensive Guide to the Sunny Side of Chess Endgames.” Beyond that section, the book is a wonderful resource for surprising endgame devices and ploys. An earlier work that inspired the same love for endgame stratagems is Jenö Bán’s “The Tactics of End-Games.” It too offers a hoard of insightful endgame ruses.

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• Try these mate in two problems on for size!

• 11 months ago

lloydrook Thank you!

• 11 months ago

awesome!

• 16 months ago

Unleash_the_Queens  You know, I still haven't gotten any of them right. But give me some time. Thanks, my friend. Always good to hear from you.

• 16 months ago

E1Chu2sov Thanks!

• 16 months ago

Sunnyboya THANK YOU!

!

• 16 months ago

Nicholas_Shannon80 I don't know how you'd feel if you were actually in the class. I mean, those kids can be pretty annoying to be around. All kidding aside, thanks for brightening my day.

• 16 months ago

Remellion I appreciate your filling in some of the analysis I left out of the answer. I should have spelled out the solution more fully and clearly didn't do a good job of it. Thanks for elucidating so nicely.

• 16 months ago

Pladsen I like your interesting comment. Actually,  I think quadrivial (and quadrivium) goes back to the 15th century. For sure, Henry David Thoreau uses the word, Ben Jonson uses the word, Marshall McLuhan uses the word, and of course, James Joyce uses the word in both Ulysses and Finnegans Wake. I only used the word because I couldn't think of anything else with my deadline approaching. Thanks for your intelligent remarks and for appreciating the value of adding Ryan and Hale to the class. I must share your good thoughts with them.

• 16 months ago

Kakamou12 Correct!

• 16 months ago

goblin4563 I appeciate your adding to my good cheer this Tuesday morning. I can't wait till Wednesday. Thanks again -- Zephyr

• 16 months ago

Mike, I can't even set my watch by my articles. I don't think my old Timex is working. Nevertheless, thanks for the good cheer. You've made my Tuesday morning.

• 16 months ago

Thanks! The second one was really easy, as was the last one. The others not so much.

• 16 months ago

Thank you

• 16 months ago

NICE!

!

• 16 months ago

Thanks, professor. I enjoy being in your class.

• 16 months ago

Quadrivial indeed - the last puzzle actually has 4 lines to consider.

1. Nb5 c1=Q and 1. Nb5 Ka3 are already addressed.

1. Nb5 c1=N 2. Nc3+ Ka3 3. Rb5! with 4. Rb3# next, since the Ra2 pattern fails here.

1. Nb5 Ka5 and white has nothing better than 2. Nd4+ picking up the pawn by discovery.

• 16 months ago

Clearly I need remedial studies, since I did not find these puzzles to be trivial.

I like the play on words in the title.  However, my inner mathematician is wondering if it should be "quadruvial" (as in, double, triple, quadruple, etc.). The other prefix I know of for four-ness, tetra, leads to tetravial, which is too weird even for me.

After further reflection, I jogged my brain enough to remember some words that use quadri as a prefix (for example, quadriceps, quadrilateral).

Speaking of fours, it was nice to see your class grow three weeks ago.  Ryan and Hale are a good complementary pair to Zephyr and Lucian.

• 16 months ago

The answer to question 4 is NO!

White can't stop black's pawn. The pawn promotes. But does white win the game? Yes he does

• 16 months ago

Pando means friday in which language?(P.S. aren't you being a little too cheerful?)

• 16 months ago

It's Pando - which means it's Friday! Double bonus

You can set your weekend calendar by his articles!