First, white can get a ko. Moves from 1 to 4 are forced. Then the order of moves can be changed, the result is still ko. If at 7 then , , , . If at 8 then , , .
But black can do better. The exchange for in the problem diagram is bad style as it's not necessary. If black starts with this 1 white dies.
Thanks a lot. I found the ko and Black's improvement, but I didn't deduce the bad style move because I didn't think about the last diagram. It is remarkable how a higher dan's answer combines accuracy and conciseness. --Dieter