threatens to make life in the corner, while creating approaches to the existing liberties. If Black threatens the connect-and-die at 3, White simply blocks, and
is a necessary approach move, allowing White to win the semeai (which then stands at 2 liberties each).
If Black plays at directly here, a either reverts to the previous diagram (or else Black will have to connect at c, and White wins anyway); and b also wins, more directly (even if Black gives atari on the next move, White simply connects, and Black is caught in double damezumari). I haven't worked out whether it makes a difference in points, though.
xela: Intuitively, b feels more pleasing to me than a--but either way, d is going to be sente for black, so in terms of points and number of ko threats it's identical--I can't see any reason why either move is better than the other.
looks like the right way to exploit the shape, by analogy with problem 4, but after
, it seems that the best White can do is to set up a ko.