Gokyo Shumyo, Section 1, Problem 31 / Solution

White lives  

makes an eye at a and makes miai of b and c for the second eye. It is clearly the vital point.

Wrong 1  

One technique to live is to enlarge the eyespace, which is the purpose of . However, in this problem this technique does not work, because the push at followed by the placement at the vital point of kills. Despite and further enlarging the eyespace, and can reduce White to only one eye.

Wrong 2  

makes an eye where there is already one. It is not vital. Black can now kill by playing either of or .

Here we present killing by . After , the placement of results in White having only one eye.