Gokyo Shumyo, Section 2, Problem 1 / Solution

Main line  

makes miai of and for killing the group. This is the main line, although the following variations offer equal resistance. The problem is an application of the well known L + 1 group and the life and death proverb there is death in the hane.

Variations

Variation at 4  

If here, makes a false eye.

Variations at 2  

More interesting is Black's resistance at . makes miai of and . can also be played at , making miai of and a. This shape may appear as a seki to the untrained eye, but the Black group is dead, because he'll have to fill at a, after which his eyespace is almost filled with a killing shape of straight three. (See the addendum at rectangular six in the corner.)

Variations at 2  

After , kills. at a also kills.

Failures

Failure 1: life with points  

Without the marked stone's presence, this line of play would also work for White because she's able to cross under at a (and Black cannot benefit of the usual shortage of liberties of this shape, due to his own shortage). Now, however, White a would be self-atari. Incidentally, there is no ko if White continues now at b.

Failure 2: seki  

strikes at another vital point of Black's corner, but again prevents a connection underneath and Black has time to enlarge his eyespace at . Some people may falsely recognize a bent four in the corner: there is none, due to the extra eyespace at the marked point.

Failure 3a: ko  

After , ko is the best result for both. Here, White is able to start the ko but the ko is not direct for her.

Failure 3b: ko  

Another variation leading to ko. Note that White must play here, forcing to start the ko, allowing White to take the ko first.

Failure 3b continuation  

After takes the ko, gives no resolution. Black must now play the ko at the marked stone. Now he can start the ko, but unlike variation 3a, the ko is direct for White (see direct ko).