$$Wc White to play and win
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | . O X 3 X O O |
$$ | O X X . X . . |
$$ | O X . X . X 1 |
$$ | O X X . X X 2 |
$$ | . . . . . . . |
$$ ---------------
- Click Here To Show Diagram Code
[go]$$Wc White to play and win
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | . O X 3 X O O |
$$ | O X X . X . . |
$$ | O X . X . X 1 |
$$ | O X X . X X 2 |
$$ | . . . . . . . |
$$ ---------------[/go]
Usually

is part of a combination with a connection along the edge that gains 1/2 pt. Here it is part of a combination with

, which gains 7/12 of a point. White wins by 1 pt. The rest is miai.
$$Wc Stubborn resistance
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | 9 O X O X O O |
$$ | O X X 6 X 5 4 |
$$ | O X . X . X W |
$$ | O X X . X X X |
$$ | . 7 8 . . . . |
$$ ---------------
- Click Here To Show Diagram Code
[go]$$Wc Stubborn resistance
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | 9 O X O X O O |
$$ | O X X 6 X 5 4 |
$$ | O X . X . X W |
$$ | O X X . X X X |
$$ | . 7 8 . . . . |
$$ ---------------[/go]

offers the most stubborn resistance by capturing a stone. The point of the exercise is that

forces

, so that the combination,

-

, gains only 1/3 pt. Now the combination,

-

, gains 1/3 pt. for White. The players share the two open kos. White still wins by 1 pt.
The original position has an overall count of -5/12 (from Black's point of view). After

-

the count is -1, for a White win.
$$Wc Failure
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | 7 O X 1 B O O |
$$ | O X X 9 B 2 3 |
$$ | O X . X . X 4 |
$$ | O X X . X X . |
$$ | 8 5 6 . . . . |
$$ ---------------
- Click Here To Show Diagram Code
[go]$$Wc Failure
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | 7 O X 1 B O O |
$$ | O X X 9 B 2 3 |
$$ | O X . X . X 4 |
$$ | O X X . X X . |
$$ | 8 5 6 . . . . |
$$ ---------------[/go]

fills the ko.
The right and center look like a miai pair, each of which gains 1/2 pt. However, they interact because of the threat against the

stones in the previous diagram. If White makes the mistake of playing them as miai (

-

), he loses 1/12 pt., for a count of -1/3. Then each of

-

gains 1/3 pt., so that the count remains -1/3.
Now White has no ko threat, but must fill a dame with

. (Note that

was necessary to prevent

from becoming a ko threat.) Then

fills the ko to gain 1/3 pt. for jigo.
$$Bc Black to play
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | . O X 1 X O O |
$$ | O X X . X . 4 |
$$ | O X . X . X 2 |
$$ | O X X . X X 3 |
$$ | . 5 . . . . . |
$$ ---------------
- Click Here To Show Diagram Code
[go]$$Bc Black to play
$$ ---------------
$$ | . . . . . . . |
$$ | . O O O O O . |
$$ | . O X 1 X O O |
$$ | O X X . X . 4 |
$$ | O X . X . X 2 |
$$ | O X X . X X 3 |
$$ | . 5 . . . . . |
$$ ---------------[/go]

gains 7/12, for a count of 1/6. Now the combination,

-

, gains 1/2, for a count of -1/3. Finally,

gains 1/3, for jigo.
