I've been studying the tesuji book mentioned in this thread: http://www.lifein19x19.com/forum/viewtopic.php?f=17&t=1503

I can't read the text, but I can usually follow the answer diagrams well enough to understand what's going on. But this problem has me stumped:

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . X . . . O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Here is the supposed zokusuji:

Click Here To Show Diagram Code

[go]$$Bc zokusuji
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . 1 X . . . O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

And the correct variations:

Click Here To Show Diagram Code

[go]$$Bc Honsuji 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O 1 . . . . |
$$ | . . . . . . . . . . . 3 X 2 . 4 O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Click Here To Show Diagram Code

[go]$$Bc honsuji 2
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O 1 . . . . |
$$ | . . . . . . . . . . . a X . 2 . O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

I understand the throw-in makes sente, but I don't see why that's better than this:

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . 3 X 1 2 . O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

And it seems like the whole area is basically dame anyway, how can white do anything besides this:

Click Here To Show Diagram Code

[go]$$Wc Black to play
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . 2 X 1 . . O O . |
$$ | . . . . . . . X . O . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Can someone help me see the light?

Your last diagram is suboptimal for white, and is the source of your confusion, I think.

White can do better, white can cut:

Click Here To Show Diagram Code

[go]$$Wc White cuts
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . 1 X . . . O O . |
$$ | . . . . . . . X . W . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

And, because of the marked stone, the cut is sente. Try out some variations to see why the cutting stone can't be captured, and what the value of is.

Black's goal, therefore, is to protect against the cut . But more than that, black would like to do it in sente.

Simply connecting is gote, so that's not good enough.

In your "honsuji 1" diagram, black has connected against the cut, and gets sente after .

In your "honsuji 2" diagram, the presence of defends against the cut, because now black can capture the cutting stone by driving it towards the edge. So again black has sente.

White has a honsuji himself if it is his turn. Knowing that one exists, can you find it?

With that in mind, I believe the reason the throw-in at in your second diagram is good is because it allows black to patch his weakness in sente. If we're in the endgame, playing here could be double-sente.

in your second diagram is a very nice honsuji I've never seen before. I quite like it.

Edit: Ninja'd by herman, but I've already typed all this up, so I'll post it.

_________________
We don't know who we are; we don't know where we are.
Each of us woke up one moment and here we were in the darkness.
We're nameless things with no memory; no knowledge of what went before,
No understanding of what is now, no knowledge of what will be.

Thank you both, I completely missed white's tesuji. This makes a lot more sense now.

Minor nit: At the time when this play is likely to be made, the White capture will probably be sente. But that would make this a double sente, and double sente depends on the circumstances. Theoretically, this is Black's sente.

Click Here To Show Diagram Code

[go]$$Wc White cuts
$$ ---------------------------------------
$$ | . . . . . . . . . . . 3 . O . . . . . |
$$ | . . . . . . . . . . 2 1 X . . . O O . |
$$ | . . . . . . . X . W . X O O O O X O . |
$$ | . . . , . . . . X , . X X X X X X X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

I think that, theoretically speaking, Black should play to generate aji and then play elsewhere.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.