Gokyo Shumyo, Section 1, Problem 57 / Solution

Traditional Solution  

threatens a double atari at , in which case White escapes. Next White occupies the vital point at . In terms of life and death, the points a and b are now miai, while the circled point provides an eye.

Alternative Solution  

here also lives. a and b are miai.

(The exchange White b and Black c does not affect the solutions. The resulting shape is a notcher with code 213WN.)

Failure at 3  

For someone familiar with notchers, it is clear that is not the correct way to make the group live. becomes the vital point.

Failure at 1  

This fails: Black takes the vital point and reduces the shape to six on the second line which is dead. (Incidentally, if we make the exchange White a - Black b, this is a notcher of code 123NN with the same result.)

Variation at 2 (escape variation A)  

If Black permits the double atari, after White 7 at the marked stone, he faces either the capture at a or the escape at b.

Variation at 2 (escape variation B)  

Black could answer the double atari with . White gets out in this variation, but Black can still attack later on, perhaps with a.