Corresponding squares. Is it hard?

Here the complete solution of this Study

White to play and win.

http://www.jmrw.com/Chess/Kloch/base.htm

There are positions were having the opposition loses, but can be solved through the theory of corresponding squares. Triangulation is a simple example of corresponding squares, but the theory is much more complex than that.

The study is pretty much Lasker's.  Lasker put the White king on a3 and the Black King on a8.  Reichelm's modification is to put the White king on a1 and the Black King on a7.  The corresponding squares are exactly the same.  Reichelms modification is thought to further elevate the theoretical value of Lasker's original study.  Lasker showed Reichelm his original study in 1901, then in 1937 Reichelm showed Lasker his modification.  In the original study White's first move Kb2 takes the traditional opposition (although opposition has nothing to with the solution) In the Reichhelm modification Black has the opposition and his modification highlights the irrelevance of traditional opposition.

According to Averbakh and Maizelis the Lasker study played an historic role in the development of pawn endgame theory.  At that time the teaching of opposition held undisputed sway, and the Lasker position attracted enormous attention and pretty well knocked the supporters of opposition theory off their feet.  An earlier study by Locock demonstrating co-ordinate squares in 1892 had passed unnoticed.  Chigorin was one of the first to point out the importance of co-ordinate squares.

I have just added the solution of the study of Emmanuel Lasker & Gustavus Charles Reichhelm - 1901 here :

http://www.jmrw.com/Chess/Kloch/base.htm

(use Internet Explorer)

White to play and win.

Is it winning? (White to play)

Another example of corresponding squares:

White to play and draw

Another surprising example:

Anti-opposition solved by corresponding squares

Graphic here : http://www.jmrw.com/Chess/Kloch/base.htm

How can you draw numbers on a chessboard like the one in post 5 by Tantale? And afterwards print it out? It looks very cool!

What software is used?

For this example that come from a game between Gulko and Short :

I tried to find corresponding squares.

See : http://www.jmrw.com/Chess/Kloch/base.htm

Do you think it is correct?

Thanks to help me.

Look at this study dealing with corresponding squares:

This Study of Mikhail Afanasievich Zinar can also been solve with corresponding squares theory

White to play and draw

Solution : http://www.jmrw.com/Chess/Kloch/base.htm

Can somebody understand this win ?

Maybe with corresponding squares.

He would have answered !

What I see is a mutual Zugwang exercise, where any move now by Black collapses the position. My 2 questions thus are:

1. Was this an exercise or a computer played position to demonstrate tactics?

2. Why does Black not try to win by holding opposition?

Consider the following ending:

Thanks but he would not have answered that!

Left this link earlier:

http://www.k4it.de/index.php?topic=egtb&lang=en

Sorta "cheating" but one can easily look at many lines.

The first one wins for white, or draws if black to move.

The 2nd one draws regardless of whose move, but if black moves 1st, he either draws or loses, if white moves first, he either draws or loses.

Such is too complex for me to understand fully, but can get the general idea.

He would have explained it!

Another example