Could it be that the problem has been wrongly purported?
Has s.o. the original source at hand, i.e. an online link or so?
E.g., if Blacks 1st line string has 1 liberty more it doesn't work (i.e. W's resistance),
or if W has a tigermouth on the 2nd line, Black could atari A14 on B14 (for connection of 2 black groups, thus relevant),
THUS W had to answer the atari @ B13 and
Black would gain a tempo,
for playing A18, being back in the standard line.
Alternatively, if Black had 1 more stone (or liberty) at D13,
then B could play the clamp tesuji F18 (ff) to start with.
$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O . . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | 1 O X X . . . . . .
$$ | . . O . . . . . . .
$$ | . W . . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O . . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | 1 O X X . . . . . .
$$ | . . O . . . . . . .
$$ | . W . . . . . . . .
$$ | . . . . . . . . . .[/go]
$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O O B . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O O B . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]
$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O . . . . . . . .
$$ | . . W . . . . . . .
$$ | . . . . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O . . . . . . . .
$$ | . . W . . . . . . .
$$ | . . . . . . . . . .[/go]
(this one NOT working, just for reference)
$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O . . . . . . . .
$$ | . . . B . . . . . .
$$ | . . W . . . . . . .
- Click Here To Show Diagram Code
[go]$$Bc Black to play and kill
$$ -------------------
$$ | . . O O . . . . . .
$$ | . X O X O 1 . . . .
$$ | . X O X . . . . O .
$$ | . X O X . . . O . .
$$ | . X O X . . . . . .
$$ | . O X X . . . . . .
$$ | . O . . . . . . . .
$$ | . . . B . . . . . .
$$ | . . W . . . . . . .[/go]
As this (intended tesujis and involved resistances) is fairly easy stuff for high dans,
I rather are convinced that some small yet relevant error in notation has spotted correctly.
[Being @ work - or not ?!

I do not have the resources at hand to consult the books ]