Tricky chess problem (ELO1700) - corresponding squares

My thought on this is that in a race to the key squares, Black is closer. But black does not want to "win" the race. Black wants to arrive at the blocking square after White's move so that White is forced to back off. This is similar to the concept of opposition.

White's route to the win goes through f4 or c5. When White arrives at one of these squares, Black wants to move to h5 or e7 respectively. It gets tricky if Black uses his proximity to e7 to get there first. With White King on c5 and Back King on e7 with Black to move, Black loses because he must either move away allowing White to penetrate on d6 or continue to block on d7. If that happens White will go for f4 and get there before Black can get to h5.

Black can hold a draw if he loses a tempo when necessary so that he arrives at the blocking square after white arrives at the entrance square. As mentioned above, it is then White's move and he must move away.

Here's one (relatively simple) example line: 1. Kb1 Kg7 2. Kc1 Kg6 3. Kd2 (White can still go either way.) ... Kg7! (losing a tempo) and now 4 Ke3 Kg6 and if 5 Kf4 Kh5 or 5 Kd4 Kf7 6 Kc5 Ke7.

It's not exhaustive analysis but I think it illustrates the point.

For White to win he must lose a tempo in relation to Black so Black will be forced away on his move. I haven't searched the position to see how White might force this, but it can result in a fascinating dance of the Kings.

Good luck with it ...

Hi webmeister, first of all - thanks for taking the time to explanation the situation. Apparently (according to the mentor problem) the only winning move for white is: Ka2. All other moves result in a draw.

You have to calculate this using corresponding squares (CS) but I don't know how. Do you have a good understanding of CS and how to apply it in this case? From the sound of it, I think it needs to be calculated to the exact correct move...

Honestly, I never heard of "corresponding squares" before I read your post. My best guess is that they are related to the concept of "opposition" except that instead of the Kings being separated by one square, there can be many squares between them. But the goal is to maneuver your King so that when they are separated by one square it is your opponent's move and he must give way. That's the best explanation I can come up with.

I didn't look into the position to try to really analyze it beyond what I wrote above. I could guess that because of the fact that the exercise was looking for a specific move or series of moves, that there presumaby is a win in there somewhere.

As far as how it is calculated, I don't know other than what I wrote above, which is not adequate in the context of the exercise. I probably would have yielded a draw if that had been my game.

Follow up. Perhaps this can shed some light on the beast.

https://en.wikipedia.org/wiki/Corresponding_squares

(Google is your friend)

Hi folks,

I know I'm late to the party, but as no one posted a solution so far, I thought I'd try my hand at it.

Firstly, we should notice that corresponding squares are in fact unrelated to the concept of opposition: they will vary entirely according to the position, and sometimes the right move in a corresponding square-situation will be to even give away the opposition (which Dvoretsky, in his Endgame Manual, calls "the anti-opposition".

So, in the situation here presented, we have to analyze everything before deciding on which squares correspond to which. Here is my take on it:

As pietman remarked, there is a correspondence between c5 and e7, and also one between f4 and h5. Looking further, we can see a correspondence between d4 and f7: if I play my king on d4, Black must be ready to either go to e7 in response to Kc5, or to g6 if Ke3. 

So far we have: (c5-e7) - (d4-f7) - (e3-g6) - (f4-h5)

d3 touches both d4 and e3, so its corresponding square is the one that touches both f7 and g6: g7.

c3 touches both d4 and d3: corresponding square is either f8 or g8.

d2 touches both d3 and e3, so Black needs a square touching both g7 and g6: f7

e2 touches both d3 and e3 as well, but here Black is unequal to the task: he would like to go to f6, but alas, it is impossible! 

And thus we have the solution: play the king to e2, see where Black goes, then answer accordingly. For instance:

1.Kb2 Kg7 2.Kc3 Kf8 3.Kd2 Kf7 4.Ke2 and black must yield: 4...Kg7 [4...Kg6 5.Ke3!] 5.Kd3 Kf7 6.Kd4 Ke7 7.Ke3! and it's all over.

I hope this was helpful, and that there were no faults in my reasoning.

Cheers.

Hi beckerqueiroz

Thanks for your input. I believe the only correct answer is Ka2.

I have drawn the corresponding squares below.

Could someone please let me know if it is indeed correct.

Thanks