This is a difficult variant of a classic tsumego that showed up in my recent lesson with Oscar.
Black to play.
Solution
Solution (1) The hane of 1 is one way for the black group to live. If White descends to 2, Black jumps to 3, making a miai of ‘a’ and ‘b’.
Solution (2) Things get more complicated if White responds to 1 with the diagonal of 2. Black again intercepts with 3, but then white 4 tries its hardest to set up a kō. However, with 5–7, Black can then turn the corner into a double kō life.
Solution (3) It turns out that the block of 1 here works, too. After white 2, Black attaches at 3. If White responds to 3 with 7, then black 5 forms a gote seki life. If White instead resists with 4 and 6, and, following . . .
Solution (3, contd.) . . . after 8–11, White can only cut at ‘a’, which again leads to Black’s double kō life.
Solution added – there were two, in fact!