Pandolfini's Puzzler #48 - The Fortress and the Cage, Part 3

Professor: Class, how wondrous to see you!

Here, the burble of garbled voices seemed to say pleasant prattling things back to the professor.

Professor: They say all good things must come to an end, and that’s the case today.

Thomas: Are you leaving us, Professor?

Hale: I was just getting used to your jokes.

Lucian: Actually, I don’t always understand them.

Ryan: I’ll miss those jokes, but I’ll miss you most of all.

Zephyr: Who are you, Dorothy saying goodbye to the Scarecrow in "The Wizard of Oz"?

Professor: I’m not leaving you. But I’d like to leave the topic of the past two weeks: fortresses and cages.

Lucian: Is there anything more to say on the subject?

Professor: I think so. Last week we explored caging the enemy king.

Rachel: Oh, I liked that theme.

Thomas: Me too.

Professor: Me three. Now let’s look at some problems that cage other things.

Question 1: Does White have a positional draw?

Thomas: That’s an interesting idea.

Hale: So kings aren’t the only units that can become caged.

Rachel: Here, in a way, Black is reduced to insufficient mating material.

Ryan: In a way.

Thomas: Can we see another problem?

Professor: OK. Try on this confining cage for size.

Question 2: Can White save the position?

Ryan: What a bizarre problem!

Hale: Who knew such strange things could befall an innocent rook?

Zephyr: Innocent? It must have been complicit in something.

Professor: Let’s see if you can be complicit in solving the next problem.

Question 3: Does White have a positional draw?

Lucian: That’s incredible!

Zephyr: No, it’s quite credible.

Thomas: It’s even like a fortress.

Ryan: It’s also like a cage.

Professor: It’s both.

Zephyr: Can we see a related problem?

Professor: I prefer a problem that’s not unrelated.

Question 4: Can White create a fortress and a cage?

Hale: Egads. That king is doing yeoman’s service.

Zephyr: Oh, so that’s what it’s doing.

Professor: Let’s do one more problem and put the subject to bed.

Lucian: We might as well. It’s putting me to sleep.

Question 5: Can White get a draw?

Ryan: Wow! This last problem makes me feel walled in.

Rachel: I feel as if I’ve run into a wall.

Hale: At least you’re not against the wall.

Lucian: Or up the wall.

Zephyr: Or off the wall.

Thomas: Or driven to a wall with no place to go.

Professor: So let’s go home. Class dismissed!

Answers below - Try to solve ProfessorPando's puzzles first!

 

ANSWER #48

Answer 1: White can achieve a positional draw. After 1. Bf7! Rxg7  2. g6, Black’s rook is unable get out of its cage and White can hold the position. For example, the white king can hang out in the queenside corner, shifting between a2 and b1.

If Black ever stations his king on c2 (to stop the white king on a2 from moving to b1), White can play Bf7-b3+, and after Black moves the king out of check, White can reseal the cage with Bb3-f7. The rook remains imprisoned and Black can make no progress.

Answer 2: White’s peculiar drawing idea begins with  1. c6. After 1…bxc6 (1…Rd8  2. c7 and White is OK) Kxc6, a strange situation arises. Whether Black moves the rook to a5 or d8, the white king can constantly assail it. It’s as if the rook is trapped in a cage of four squares (a5, a8, d8 and d5). 

Meanwhile White’s king can use its own four-square block (b6, b7, c7 and c6) to launch ceaseless attacks on the rook.  

From the starting position (created by problemist Robert Brieger), a sample variation is 1. c6 bxc6 2. Kxc6 Rd8  3. Kc7 Ra8  4. Kb7 Ra5  5. Kb6 Rd5  6. Kc6, and we’re back where we started. The rook can’t break out of its bizarre cage.

Answer 3: White can hold a positional draw after 1. Kc6. This prevents the black king from going to d7. It also readies a dangerous confrontation with the rook: Kc6-b7.

If Black answers 1...Rc8 (stopping 2. Kb7 because of 2…Kd7), White continues to shut out the black king by 2. Kd6, when 2...Kf7 (or 2…Kf8) allows 3. Kd7 and an instant draw. And if Black replies to 2. Kd6 by 2…Ra8, White has 3. Kc6, and Black has gained nothing.

So White has the rook in a weird two-square cage (a8 and c8), while at the same time the white king fortresses out the black king by keeping an eye on d6 and d7. It’s just another one of those crazy positional draws.

Answer 4: If White does nothing special, Black gobbles the b-pawn, with an easy win. It looks absurd, but the correct response is 1. Nxa2!, even though 1…bxa2 ensures that Black will queen. Even so, White can still survive.

After 1. Nxa2 bxa2, a sample continuation is 2. Kc1 a1=Q+ 3. Bb1! (yes, voluntarily putting the bishop in a pin). It’s remarkable, but Black has no way to extricate the queen, nor can the black king penetrate White’s stockade. The white king merely dances between c1 and c2 until there’s a threefold repetition. Once again, White has manufactured a doubly shielding positional draw, armored by a cage and a fortress.

Answer 5: White can’t catch the h-pawn (being unable to get inside the pawn’s “square” or “quadrangle”). But White has an unusual path to a draw.

White saves the day with 1. c4!. Black then has two main replies. Black can play (a) 1…bxc4, or (b) 1…h5 (the most interesting line).

If 1…bxc4, a plausible continuation is 2. a4 h5  3. a5, and White queens first, with check.

After  1. c4! h5, the astounding conclusion would be 2. cxb5 h4  3. Kb3! h3  4. Ka4 h2  5. b3! h1=Q (or any black move, for that matter), and it’s stalemate. Unbelievably, White has caged his own king — a tactic various endgame authorities describe as “walling in.”

Take note
It’s easy to view the endgame phase of chess as being dry and straightforward. Much of the time the play seems to revolve around clear-cut methods of converting extra material and other advantages into controllable wins. But it’s remarkable how tactical the final phase can be.

While there is a natural tendency to examine winning endgame stratagems, there also is a slight aversion to studying ideas that only draw. But beyond their fascination for purists, such motifs have great practical value. They can save games, and half points are always better than no points.

---