Here Black even lives in sente.
Reuven: I think it's alive like this as well, such a lively form :) But here almost any addition of a white stone and some of b stones make it killable... Would you like to change the original problem into a solvable one?
togo: But this is solvable: Solution seems to be that Black is unconditionally alive without seki. The problem is also interesting. So why replacing this problem? Adding interesting variations on the other hand is always an option. Asking for best play would be nice too. And is in the third diagram the best answer?