The book Graded Go Problems for Dan Players Volume Five contains the following tesuji problem/capturing race. Black to play, any ladder towards the right works for Black, any ladder towards the left works for white.
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O . O O O X X X . |
$$ . . X O . . . X X O . O . |
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- Click Here To Show Diagram Code
[go]$$Bc
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O . O O O X X X . |
$$ . . X O . . . X X O . O . |
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$$ . . . . . . . . . . . . . |[/go]
The white N16 group and the black S16 group are fighting for life and death.
The first correct move is N15, no questions here.
$$Bc
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O . O O O X X X . |
$$ . . X O . . B X X O . O . |
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- Click Here To Show Diagram Code
[go]$$Bc
$$ +---------------------------+
$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O . O O O X X X . |
$$ . . X O . . B X X O . O . |
$$ . . . . . . . . . O . O . |
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$$ . . . . . . . . . . . . . |[/go]
The sequence given as the solution is the following, white is caught in a ladder. Fair enough.
$$Bc
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O 7 X X O O X . |
$$ . . . X O 5 O O O X X X . |
$$ . . X O 2 6 1 X X O . O . |
$$ . . . 3 4 . . . . O . O . |
$$ . . . . 9 . , . . . . . . |
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- Click Here To Show Diagram Code
[go]$$Bc
$$ +---------------------------+
$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O 7 X X O O X . |
$$ . . . X O 5 O O O X X X . |
$$ . . X O 2 6 1 X X O . O . |
$$ . . . 3 4 . . . . O . O . |
$$ . . . . 9 . , . . . . . . |
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$$ . . . . . . . . . . . . . |[/go]
But what happens when white

is placed at M16? What can Black do now?
$$Bc
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O 2 O O O X X X . |
$$ . . X O . . 1 X X O . O . |
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- Click Here To Show Diagram Code
[go]$$Bc
$$ +---------------------------+
$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O . X X O O X . |
$$ . . . X O 2 O O O X X X . |
$$ . . X O . . 1 X X O . O . |
$$ . . . . . . . . . O . O . |
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$$ . . . . . . . . . . . . . |[/go]
The first intuition for Black is the cut at L15.
$$Bc
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$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O 7 X X O O X . |
$$ . . . X O 2 O O O X X X . |
$$ . . X O 3 4 1 X X O . O . |
$$ . . . . 6 5 . . . O . O . |
$$ . . . . 9 . , . . . . . . |
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- Click Here To Show Diagram Code
[go]$$Bc
$$ +---------------------------+
$$ . . . . . . . . . . X O . |
$$ . . . . . X X . O O . O X |
$$ . . . X X O 7 X X O O X . |
$$ . . . X O 2 O O O X X X . |
$$ . . X O 3 4 1 X X O . O . |
$$ . . . . 6 5 . . . O . O . |
$$ . . . . 9 . , . . . . . . |
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$$ . . . . . . . . . . . . . |[/go]
However, as the ladder towards the left favors white, black cant capture white this way. In fact, the book describes this exact sequence as a wrong answer for Black, but it doesn't show a correct move for Black in this situation.
My question is then, what is the correct Black response to

at M16? I can't find any move that would work. In fact, the only other candidates are N17 and M15 and these seem to fail immediately. Am I missing something or is the book mistaken?