Here's a problem from my lunch-time game on KGS. White has just played

, how should black kill? (Is it even possible to kill?)
$$Wc Black to Respond
$$ | O X X X O . X . O O O X . X X X O . . |
$$ | X . X . X X X O O X X X O O X O . . . |
$$ | . . . X . . . X O O . X X O O . O . . |
$$ | . . . . . . . . X X . X O O O O . . . |
$$ | . . . X . . . X . , X . X X O X O O . |
$$ | . . . X . . . . X X O O X X X X X O . |
$$ | . . . . . . . X O O . . O 1 . . . X O |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$Wc Black to Respond
$$ | O X X X O . X . O O O X . X X X O . . |
$$ | X . X . X X X O O X X X O O X O . . . |
$$ | . . . X . . . X O O . X X O O . O . . |
$$ | . . . . . . . . X X . X O O O O . . . |
$$ | . . . X . . . X . , X . X X O X O O . |
$$ | . . . X . . . . X X O O X X X X X O . |
$$ | . . . . . . . X O O . . O 1 . . . X O |
$$ | . . . . . . . . . . . . . . . . . X . |
$$ +---------------------------------------+[/go]
In the game, I managed to kill white's invasion. When I went over the game, afterwards, I realised that I should have stopped it entirely, several moves earlier. I also realised that white could have lived and possibly cut off my lower-right group. In fact, I couldn't find a move for black that would prevent white from doing so.