Here is the published solution for Hitachi Number 9.
After Black 1, a and b are miai.
In this variation, White cannot play at c because of a shortage of liberties.
Once Black connects the square-marked group to the circle-marked stone White can not keep these stones from escaping into the middle of the board where they can (presumably) link to a strong black group or make two eyes.
Thanks for the comment. I'll amend the original problem to include this assumption.
The following variation aroused a bit of debate in rec.games.go. Apparently the published solution did not show how to continue after Black 3...
How should Black continue? He must not let White play a and b or else Black will die. Black can keep White from connecting by playing at a, b, or c. At c is my current preference:
White's marked group only has six liberties while Black's marked group has at least seven.
Can anyone improve on this?
This sequence is confusing: Move number 9 prevents White from playing at a in sente, but lets White live with 10. Black could kill White by playing at 10 himself.
White 2 makes one eye and now threatens the connection at a or the second eye at b. However, she has a weakness at c, as shown.
unkx80: The fight need not be so complicated. =)
A second possibility:
That's why in my humble opinion Black 5 is a better answer: after Black destroys White's eye shape with 9, White a is no longer sente for connection . White a and b are miai killing the white group:
The above demonstrated that White ''a' is an overplay. So, White captures at 1, Black 2 recaptures at the marked spot ...
White 3 recaptures yet again - it's not a ko - and her stones are all connected. Although the marked white stones in the corner are dead, White still has the aji of the ogeima at b, so Black's corner is not too big. In the "capturing race" diagrams, White loses a lot of points compared to this diagram.