The position below is adapted from a recent game of mine. White has just passed, so it is black's move. White could have played j15 as the dame were being filled to fix the bad aji of the 2 black stones inside white's area, but then he would have lost by 0.5 points (Japanese rules). But bad aji won't win the game for black, he must find a sequence that works against any white resistance. The stakes could not be higher!
Note that a ko can be assumed as a success for black, as he only needs to gain 1 point to win the game, and there were indeed threats on the rest of the board. I have studied this position extensively and I believe black can win, though it is possible I missed something. This is a hard problem, to solve it without playing it out I think you need to be a high dan. I will give a few hints below, and post my solution later.
$$c Black to play
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$$ | . . X X X O . . . O X . . . . . . . . |
$$ | . . X O O . . . . O X X . . . , . . . |
$$ | . . X O . . . . . X O X . . . . . . . |
$$ | . . X O . . . . . . O X . . . . . . . |
$$ | . . X O . . . . O O O X . . . . . . . |
$$ | . X X O . . . X O X X X . . . . . . . |
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$$ | . X O O O X X X . , . . . . . , . . . |
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$$ | . X X X X X . . . . . . . . . . . . . |
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[go]$$c Black to play
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$$ | . . . . X O . . . O X . . . . . . . . |
$$ | . . . . X O . . . O X . . . . . . . . |
$$ | . . X X X O . . . O X . . . . . . . . |
$$ | . . X O O . . . . O X X . . . , . . . |
$$ | . . X O . . . . . X O X . . . . . . . |
$$ | . . X O . . . . . . O X . . . . . . . |
$$ | . . X O . . . . O O O X . . . . . . . |
$$ | . X X O . . . X O X X X . . . . . . . |
$$ | . X O O . O O O X X . . . . . . . . . |
$$ | . X O O O X X X . , . . . . . , . . . |
$$ | . X O O O X . . . . . . . . . . . . . |
$$ | . X X X X X . . . . . . . . . . . . . |
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