Gokyo Seimyo Volume 3 Problem 8 / Attempts

Vital point  

The move 1 seems to be the vital point. Plausible responses seem to be a, b, and c

First follow up  

After the exchange of 1 & 2, if black b then

sente seki  

Black can only survive in gote in a seki. Move a is better since...

Anon: I'm confused how this is seki. Surely W will eventually fill up all outside liberties, and then can atari with a dead shape by playing above ?

sacrifice 3 stones  

White captures three stones for 6 points, while black lives with 4 points (assuming black cannot play ko for the whole group). This is 2 points worse than the seki variation, but black gets sente. It will normally be the best variation for both sides.

black 1 variation  

Black 1 here leads to the same 3 stone sacrifice

black 1 variation  

This black move dies since after 4 black cannot connect his 3 stones and black is left with only one eye around the captured white 2. Black could live with 3 at 4, but they get only two points while losing the corner part of their group.