Pandolfini's Puzzler #42 - Trivial or Quadrivial?

  • NM brucepandolfini
  • | May 16, 2014

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.

bishop_evil grin white.png

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.


  • Some of these checkmates are strange - make sure you know different mating patterns in our course on checkmate;
  • If you mate with a knight, you may just win one of our 56 site awards - how many have you won?
  • Try these mate in two problems on for size!


  • 2 years ago

    NM brucepandolfini

    lloydrook Thank you!

  • 2 years ago



  • 2 years ago

    NM brucepandolfini

    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.

  • 2 years ago

    NM brucepandolfini

    E1Chu2sov Thanks!

  • 2 years ago

    NM brucepandolfini

    Sunnyboya THANK YOU!


  • 2 years ago

    NM brucepandolfini

    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.

  • 2 years ago

    NM brucepandolfini

    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.

  • 2 years ago

    NM brucepandolfini

    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.

  • 2 years ago

    NM brucepandolfini

    Kakamou12 Correct! 

  • 2 years ago

    NM brucepandolfini

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

  • 2 years ago

    NM brucepandolfini

    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.

  • 2 years ago


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

  • 2 years ago


    Thank you

  • 2 years ago




  • 2 years ago


    Thanks, professor. I enjoy being in your class.

  • 2 years 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.

  • 2 years 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.

  • 2 years 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

  • 2 years ago


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

  • 2 years ago

    FM MikeKlein

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

    You can set your weekend calendar by his articles!

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