In problems like #33 the point of the problem is to find the *best* move to protect the cutting point. A possible solution is a move that will enable you to capture a cutting stone with a forced sequence. You need to look at all such moves and then choose.
In #33 you mentioned F5.
- Click Here To Show Diagram Code
[go]$$
$$ |-----------------|
$$ |. . . . . . . . . |
$$ |. . . . . . . . . |
$$ |. . . . . . x . . |
$$ |. . . . . . . . . |
$$ |. X X X X 1 . . . |
$$ |. O O O O X . . . |
$$ |. O , O X X , . . |
$$ |. O . O . . . . . |
$$ |. . O . . . . . . |
$$ |-----------------|[/go]
This works but its disadvantage is that it's not efficient. A stone at F5 stops the cut but does nothing else. In particular it is the least helpful connection in the event that White plays in the upper right corner, at x for example.
We can protect the cut by backing away from the cutting point one space: the tiger's mouth.
- Click Here To Show Diagram Code
[go]$$
$$ |-----------------|
$$ |. . . . . . . . . |
$$ |. . . . . . . . . |
$$ |. . . . . . , . . |
$$ |. . . . . . . . . |
$$ |. X X X X . 1 . . |
$$ |. O O O O X . . . |
$$ |. O , O X X , . . |
$$ |. O . O . . . . . |
$$ |. . O . . . . . . |
$$ |-----------------|[/go]
This also protects the cut, but its weakness is that it allows a peep:
- Click Here To Show Diagram Code
[go]$$
$$ |-----------------|
$$ |. . . . . . . . . |
$$ |. . . . . . . . . |
$$ |. . . . . . , . . |
$$ |. . . . . 2 . . . |
$$ |. X X X X 3 1 . . |
$$ |. O O O O X . . . |
$$ |. O , O X X , . . |
$$ |. O . O . . . . . |
$$ |. . O . . . . . . |
$$ |-----------------|[/go]
The

exchange helps white. On this board white will be able to use the stone and make life in the upper right. Generally speaking, the tiger's mouth is the wrong solution when this exchange is bad for black.
The correct solution is:
- Click Here To Show Diagram Code
[go]$$
$$ |-----------------|
$$ |. . . . . . . . .|
$$ |. . . . . . . . .|
$$ |. . 9 . 7 5 , . .|
$$ |. . . 8 6 4 1 . .|
$$ |. X X X X 2 3 . .|
$$ |. O O O O X . . .|
$$ |. O , O X X , . .|
$$ |. O . O . . . . .|
$$ |. . O . . . . . .|
$$ |-----------------|[/go]
With

you can always capture a cutting stone with the sequence.

is doing double duty because it's also occupying a useful point.