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Example 1

This tesuji is quite difficult and has some interesting variations. The problem is from Sensei's, where there is a long discussion of it.

Black to capture the two white stones at "a"

These are the intersections MadLab considers while searching:

The answer is at the knight's move (marked red point) in the above figure. MadLab finds this in about 15 seconds on a fast pc, and no other black moves will work. Below we take a look at some of White's escape attempts, and how they are refuted.

The jump to White "2" in the above figure seems to escape, but Black can play in between with "3". If White ataris at "4", Black ignores the atari and counter-ataris at "5". If White captures the black stone, Black can capture White in a ladder afterwards.

What if White tries to escape with another jump to "2" in the above figure? Then Black has the tesuji at "3", and White is dead.

A similar variation happens if White tries the knights move at "2" in the above figure. After this Black first cuts at "3", and if White tries to escape with "4", playing a black move at "5" kills White.

As the last variation we will consider what happens if instead White attempts the diagonal move at "2" in the above figure. If so, Black has to come up with some precise moves. First Black forces at "3" and "5".

White may counter-attack with ataris at "6" and "8" in the above figure, but Black will only answer the first atari (with "7"). Instead of answering the last atari, Black plays the surprising tesuji at "9".

If White captures the black stone (cf. "10" in the above figure), Black answers at "11", and White is dead. White may now capture another black stone, but this does not help.

The above figures illustrate what MadLab is thinking about while solving the problem. In the process, MadLab looks through all these variations (and more). You may wonder why other Black moves than the knight's move (Black "1") do not solve the problem. These alternatives are also considered by MadLab while solving the problem, and the program can tell you why they do not work.