Beginner Exercise 212 / Solution

White kills.  

kills by making an eye in the stomach. Black cannot play a because of shortage of liberties. b and c are not real eyes -- Black cannot even fight a ko for them since there would be nothing to do if he "won" (connecting does not help at all, and no white groups are in danger). If required to prove that Black is dead, White could wait until the end of the game (when there are no ko threats) and capture at b and then c at her leisure. Of course, in a real game this sequence would not actually be played out.

White failure.  

This is seki.

Black first

Black is dead.  

does not work, since almost fills with a bulky five and Black is dead. at a does not work for the same reason. at does not work either, since then at produces the same situation analyzed above. Black cannot save this group and thus Black is dead. (So actually, we see that White need not play at -- Black's group is already dead as it stands).

The hint explained

Black lives! (5 at 1)  

Note that with an extra outside liberty, Black can live by playing at .