Gokyo Shumyo, Section 1, Problem 32 / Solution

Black lives  

The descent of is the key move; it is the only move that gives life for Black.

Continuation  

In the continuation up to , a and b are miai for life.

Wrong 1  

Simply connecting is not enough. is pretty well forcing, and after , Black has six stones on the second line.

Wrong 2  

Black's move here gives ko in various ways, of which the best one is to start by capturing. (In practice, Black may choose this line to emphasize the cutting point at a when ko threat situation favors him.)

Wrong 3  

here seemingly abandons the marked Black stone in order to secure life by playing at . However White takes him by surprise and plays at , the vital point now, herself. Whatever Black tries now, even going back at the correct move at a, the exchange of and will prove to cost him life.