The solution is to hane at ; black has to play in order to make two eye shapes; the throw-in at then starts the ko. This is a two-stage ko that is favourable for Black, in which Black can immediately capture, forcing White to find the first threat.
CW?: I'm sorry, I don't quite understand. Why can black immediately capture? If black takes isn't this a ko and black cannot capture?
symplicity:The ko rule prevents you from repeating the previous board position. If black captures , this does not repeat the board position yet. Black will have a stone at the 1-1 point that he didn't before (because did not capture anything).
CW?: Thanks. I completely misunderstood the problem. So black captures and white cannot recapture because of ko. My question then is why would white do such a thing, since now it looks like black can make life?
MrTenuki: If is played any where else, Black plays there and lives unconditionally. So, the only chance for White to kill the Black group is to fight the ko per the diagram below. (Note that the locations for , , , and are not meant to be taken literally; they denote moves played elsewhere.)
How White might win the ko: - = ko threat and reply, and = tenuki
FewKinG?: MrTenuki, I'm a bit confused about the white move in the upper right (the black one marked in my diagram), shouldn't this rather look something like this with white capturing in move 10 creating another ko?:
How White might win the ko: - = ko threat and reply, = tenuki
Because of black's eye at a connecting at b isn't good enough for white.
If white tries to play on the top first, black will just hane and make two eyes (white can't push at a or black will immediately capture).