Last one is also winning.
Corresponding squares. Is it hard?

Yes the last one is not unique.
The process involves to numerote the squares:
What is funny is that an OTB player is now allowed to take notes during a game. So he would be disqualified if he made such a drawing.
Can someone link info about this please. I dont know what this tecnique is but it seems worth learning
so how do you generate the mutual zugzwang numbers? I get once you have the diagram you have to match the numbers but how do you get the numbers to begin with? also what if the white king (on the path 3-5-3) goes back to the initial 3 square he was on?

it can be very simple or incredibly complex depending upon the position.
Hmmm, I can't decide.

The theory is described in the 1932 treatise L'opposition et cases conjuguées sont réconciliées (Opposition and Sister Squares are Reconciled), by Vitaly Halberstadt and Marcel Duchamp.
That's why I put a picture of these two men above.

An other example, this study (1901) of the world champion Emmanuel Lasker and Gustavus Charles Reichhelm:
I suggest the book "The final countdown"
http://www.amazon.com/Final-Countdown-Herman-Claudius-Riemsdijk/dp/185744129X
The entire book is all about key squares and corresponding squares.

A video wich explains the corresponding squares base on a study of Grigoriev:
http://www.youtube.com/watch?v=cwjNat39lws

Thank you Tantale for this forum and useful links.
Tablebases are good training for this sort of thing. Unfortunately limited to 6 pieces (including kings) ie 4 pawns.
http://www.k4it.de/index.php?topic=egtb&lang=en

Corresponding Squares?
It seem to me that it is called end game Opposition. It was covered in Silman's Endgame book without using, "the Corresponding phrase."
That phrase is not familiar to me and that is what makes it more confusing. I am familiar with Opposition, Triangulation and such.
Anyway here is a video suggested so that it can be understood but the person who made the video is also confused. After watching the video you are still confused I suggest not using "Corresponding Squares" and to stick to opposition and Silman's or any other end game books.


Corresponding Squares?
It seem to me that it is called end game Opposition. It was covered in Silman's Endgame book without using, "the Corresponding phrase."
Corresponding squares is a separate topic. Pandolfini's "Endgame Course" devotes two pages to it, stating only that it requires calculation and analysis.
Here an example :
All the white moves are unique to win.