Gokyo Shumyo, Section 1, Problem 6 / Solution

Main line  

makes miai of a and b to live.

2 and 3 are miai  

After , there are real eyes at the circled points.

Yes they are  

After , there are real eyes at the circled points.

White's try for ko  

What if we get the plays up to here?

Then sets up an oiotoshi. Now if White takes , Black gets eyes by playing atari at the 1-1 point.

Wrong (i)  

The other 1-2 point is not the solution. White pushes through with and plays at the vital point , making miai of a and b for the kill.

Wrong (ii)  

The 2-2 point doesn't provide life either. White pushes at and creates a situation very similar to problem 1. kills.

Wrong (iii)  

One would think that enlarge the eye space with suffices, but it doesn't. White says "There is death in the hane" and plays . After the eyespace is further reduced with , Black is left with a bulky five and White strikes at the vital point.

unkx80: After the hane at , Black effectively has an L-group.

Wrong (iii) variation  

Playing at here doesn't help Black. and can be switched.
Note: Playing at would make Black play at and White at a. This is a bent four in the corner shape and it's dead too, but if you can avoid that shape and kill in a simpler way, it is better to do so.