The solution of this problem relies on the rule that a board position can not be repeated.
Black 1 threatens to connect along the upper side (see variations). Then he threatens to make a living shape with 3, forcing White 4. Follows the awkward play at 5, needed to prevent a deadly bulky five. White must capture to prevent a lively bent four.
Of course the connection of here yields more in actual play. - TDerz
Black 7 recaptures, recreating an earlier board position. White would like to play at a BUT she is not allowed. Can someone explain why Black can do it and white can't. Probably has something to do with the difference between positional ko and superpositional ko...
Harleqin: Black has to find a threat before he may play . In the next cycle, White has to find a threat before , then Black before etc.. Thus, this is a ko fight.
What if White makes the Bulky five nonetheless. Isn't this ko? No, it isn't: Black has two outside liberties, enabling him to atari all White's stones. If White connects at the marked spot with 8 instead, she creates a living 7 point eyespace inside Black's group.
If White prevents the situation at the side, Black connects along the upper side this way or ...
In actual play, take stones directly whenever you can, keep sente and options, e.g. reserve the threat in above diagram for "a" here. - TDerz
... this way, making miai of a and b.
Bill: Are you sure that White is prohibited from continuing? Wasn't this problem constructed before there was any superko rule? My guess is that the point is that Black can connect or get an eternal life. If this is the last diagram in the solution, maybe it is just to illustrate the repetition.