This is an original problem arranged from a shape that appeared in a recent tournament game by Lukáš.
Black to play.
Solution
Failure The peep of 1 looks tempting, but is actually a mistake. After white 2, the white corner cannot be captured; black 3 is probably the strongest attempt, but after 4–8, the miai of ‘a’ and ‘b’ ensures White’s life.
White fails It is correct for Black to directly hane at 1. If White turns with 2, then 3–7 kill the group; this is a failure for White.
Solution In response to the hane of 1, White should counter-hane with 2. After Black’s inevitable cut of 3, White can then resist with 4 and 6, and after black 7 a kō for White’s life is formed at 2. This is the best either player can do.
Solution added.