Beginner Exercise 264 / Solution

Solution  

The first move is a throw-in at .

Solution  

If captures the stone, then destroys White's eye. Subsequently, a and b are miai.

Solution  

If connects here, then is an atari on the five White stones. This forces , and allows to connect back and leave White with a false eye.

Failure  

The move order is important. If black exchanges for first, then throws in at , then white doesn't need to capture, but can make a second eye with .