I tried to solve this tsumego, black is on the move:
it seems to me that white can kill black only if he wins the ko two times. Is that correct? After first ko win he will connect at 1-3 and after second win he will take at 3-2.
Black lives:
$$B
$$ -------------------
$$ | . 1 . . X O . . .
$$ | O X . X X O . . .
$$ | . X X O O O . . .
$$ | O O O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
White kills unconditionally:
$$W
$$ -------------------
$$ | . 2 1 . X O . . .
$$ | O X . X X O . . .
$$ | 3 X X O O O . . .
$$ | O O O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
This doesn't work for Black, either.
$$W
$$ -------------------
$$ | . . 1 . X O . . .
$$ | O X 3 X X O . . .
$$ | 2 X X O O O . . .
$$ | O O O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .
I think black should play 2-1 then 3-1 and 1-3 are miai for b life, no need for ko