Black lives only if White plays this sequence follishly to allowing Blace to capture at a. White can play b as , , , or even to connect to White's two stones and thus kill the main Black group even if allowing Black's few stones on left to escape if they can. The longer White delays in playing b after , the better for Black.
signal9: I'm not 100% sure, but this looks pretty good to me.
unkx80: Nah... this is a failure diagram.
YongCao? I think should play first, then .
PeiweiCao? Black dies:
PeiweiCao? Now White has two choices:
Gregory at a or b. After either choice White must next choose whether to capture Black's two stones in the corner or four stones on the left leaving the other group to make the second eye for Black. In all scenarios, it seems to me that White will be better off after to capture it and the two supporting stones and to allow Black to live have the second eye in the corner. This makes the White wall on the left solid with no cutting points.
Gregory After White can play either at or (in which case letting Black play at ).
PeiweiCao? One of the two blocks of White will be eaten, and Black lives.
PeiweiCao?: Consider white move 2 at p19 instead of m18, I believe that white p19 assures the death of the black corner.
unkx80: at ?
Gregory Yes, If Black plays at (of the previous diagram) then White has to choose between a and b to decide which group to capture and which to let live to make the second eye. The capture at a seems the obvious choice.
Alexandros?: I'm not sure if it's cheating in a problem, but White could play at in that case, and run into the wall at the other end of the board. Of course, this goes beyond the bounds given for the problem, so it may be wrong...
For your question of at , I leave it as an exercise: What is the gist of this problem? The tesuji has been mentioned on this page at least twice already...
Gregory If White plays at (of previouse diagram) then Black plays at P18 for double atari to capture the two White stones when White saves the three stones in the corner. However since Black is open on the top this is not so good for White.
Boardwalk?: Doesn't kill black. Allowing for the run to the other edge of course.
unkx80: is a mistake, should be at .
BluPian0: A tricky snapback to find. Thanks goes to Violence for helping me find the solution.
Gregory In this variation on the solution of at O19, after , White takes in corner with leaving atari on the four Black stones forcing , so White can close the top with if needed.
AVAVT: Hm... I doubt this is the proper solution. After what would you do?
AVAVT: Oh Black can still live. I didn't notice .