Problem Solving Techniques

White to move

When I am trying to figure out how strong is some of my students, and how good is his thinking technique, first of all I am trying to test them in two important things. First one is calculating technique (How I do that, I already explained in one of very first posts on this blog) and second one is how they solves problems.
To test that I usually prepare some of endgame examples, because in the endgame you can see how somebody thinks in a purest form. This is one of these examples. This position is actually very famous and you can find it in every decent endgame book which analyse endgame in encyclopaedic way (Averbah, Fine....).
I decided to show this example a bit more detailed from perspective of thinking process.
It is White´s turn in position on diagram, and he has to find an idea what to do. So, first of all and maybe most important is to find an idea. Black has full control on diagonal h2-b8 and only chans for White is to move his bishop to b8. What next?
We shall see, but first we will test what would happen if Black does nothing.
1. Bg5 With idea Be3-Ba7-Bb8. We could start with 1.Bh4 or 1.Bf6 as well
1...Bg3  Black is waiting
2. Be3, Bh2
3. Ba7, Bg3
4. Bb8 and now Black has to move from this essential diagonal.
4...Bg1 ...in order to play Ba7
5. Bg3, Ba7
6. Bf2 and White is winning because black lost control of critical square b8.
So, what we can see is that Black can not just wait and that White has a winning idea.

Better defence!

So, what can be black´s defending idea?
If White is not treating Bc7 (by moving his bishop from d8 to g5 (f6,h4) he can try to move his king to a6 and to stop transfer of bishop to b8 (via a7). Let´s try that
1. Bg5, Kb6!
2. Be3+, Ka6 ....and so far so good. Black is defending successfully.
If White tries to play back on c7, black is moving his king back to c6. So is it a draw?

White tries again

White can try with a tempo move ( Idea again):
3. Bd4 and now Black has to move his bishop from h2. Why is that important is not easy to see.
3...Bg3 ...and White is playing for Bc7 again
4.Bf6, Kb5 Black has to go to c6.
5. Bd8, Kc6 and we have a position from first diagram, but black bishop is on g3 instead of h2.
Because of this minor detail White can win a game.
6. Bh4!, Bh2
7. Bf2 and black has no time to go with king to a6. White wins by already known manoeuvre.
And again, it seems that Black is lost.

Even more resistance

Black on move

Now is time to find a new idea for Black.
Is there some possibility to fight against both of White ideas ?
Black obviously can not stay on safe square h2 because he has to play with his bishop.
He has to find square on which he can somehow distract white´s plan. So that square should provide double safety for black. White would be able to win a tempo by attacking black bishop, but would not be able to move his bishop to a7. There is one more square on b2-h2 diagonal which is as safe as h2, just because that transfer of white bishop on g1-a7 diagonal would not be possible. Of course that we can solve this by method of elimination, but that is not what is best to do. 

We have to find an idea!

3...Bd6!  All right, but why here?
4. Bf6 Remember, idea is Bd8-Bc7
4...Kb6
5. Bd8+, Kc6 ...and now White wins a tempo with...
6. Be7 ...but Black plays on his safe square h2
6...Bh2

What hapened is that there is no 7.Bc5 now (with transfer to a7) because that square is under control of black king.
We can see that Black actually has two safe squares h2 and d6!

White eventually prevails!

Position after 2...Ka6

And again, the key thing is to find a right idea.
If we goes from our initial position (diagram number 1.) and play 1. Bg5, Kb6 2. Be3+, Ka6 we have to ask ourselves a question, is it possible to take away both safe squares from black?
Of course it is. Solution is trivial.
3. Bc5! Controlling d6 and Black is again in zugzwang. He has to either lose control of square a7 by moving his king or move his bishop from safe square h2 (and it is not possible to play on other safe square d6).
Let´s say that black will move on f4 (just for illustration).
3...Bf4
4. Be7 With idea Bd8-Bc7
4...Kb6 Black has to control c7 square
5. Bd8+, Kc6
6. Bg5 a tempo move
6...Bh2
7. Be3, Bd6
8. Ba7, Bh2
9. Bb8, Bg1
10. Bf4, Ba7
11.Be3 and White wins.

Conclusion

This example is not so difficult, but when I seen that many players under IM level could not solve it without trail and error method I understood that a key thing is that not so many players plays by following idea. It is so obvious in the endgame but it is not so obvious in the middlegame.
Other thing is that solving this position is not all what you have to do with this example. 
You can combine your training by shifting position one or two files right, or one file left. you can also try with experimenting with kings. What if White king is on a8 in the beginning? There is no Bc7 threat, but Ba7 is possible with or without Ka6. 
The third thing is to shift this position left or right, and than experiment with kings. Than you can draw some conclusions about king positions and  which pawn is wining and which one is not winning.
All right, it is a job, but it has to be done.
Not so long ago, in German Bundesliga, GM Jan Smeets did not solved this problem during a game, and he lost a game which was actually draw. 
Don´t let these disasters happen to you.