Not superhumanly hard to solve like some of the other stuff I've posted. Just hopefully neat and interesting - anyone should feel free to take a shot at this . Let's first show how we get to the puzzle.

Starting position:

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[go]$$Bc Long knight
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . X . . . . .
$$ | . . X . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

White probes, black emphasizes the left, and white chooses a sharp variation.

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[go]$$Wc Sharp
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . 3 . . X . . . . .
$$ | . . X 1 . . . . . . .
$$ | . . 2 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Cut and fight:

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[go]$$Wc Fight fight fight
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . . . 6 7 . . . . . .
$$ | . . O 4 5 X . . . . .
$$ | . . X O 8 . . . . . .
$$ | . . X 9 . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Next, "a" is also some sort of joseki but black makes a different choice instead:

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[go]$$Bc Inside turn
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . . 1 X O a . . . . .
$$ | . . O X O X . . . . .
$$ | . . X O X . . . . . .
$$ | . . X O . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

And makes another interesting choice:

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[go]$$Bc Outside connect
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . . X X O . . . . . .
$$ | . . O X O X . . . . .
$$ | . . X O X 3 . . . . .
$$ | . . X O . . . . . . .
$$ | . . 2 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

And now white draws out here. Now the question is, can black save the marked stones?
Assume that ladders to the lower right are good for White, so that the cut at "a" does not cause white to collapse outright.

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[go]$$Bc Draw out
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . c X X O . . . . . .
$$ | . 4 O X O X . . . . .
$$ | . . B O X X . . . . .
$$ | . . B O . . . . . . .
$$ | . b O a . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Dan and upper kyu players should be familiar with the above shape as one that is often hard for black to escape from. Because even with the cut at "a" followed by the atari at "b", black's two stones can only get 3 liberties. White "c" is sente so white will get 4 liberties.

Nonetheless, black tries anyways:

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[go]$$Bc Black goes for it all
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . 6 X X O 7 . . . . .
$$ | . O O X O X . . . . .
$$ | . . X O X X . . . . .
$$ | . 5 X O 2 . . . . . .
$$ | . 3 O 1 . . . . . . .
$$ | . 8 4 . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

And this brings us to problem 1. Ladders to the lower right are still good for white.

-------------------------------------------------------------------------

Problem 1 - Black to play.

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[go]$$Bc Problem 1 - Black to play
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . O X X O X . . . . .
$$ | . O O X O X . . . . .
$$ | . . X O X X . . . . .
$$ | . X X O O . . . . . .
$$ | . X O X . . . . . . .
$$ | . O O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Problem 2 - what should white do instead?

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[go]$$Wc Problem 2 - White to play
$$ ----------------------
$$ | . . . . . . . . . . .
$$ | . O X X O X . . . . .
$$ | . O O X O X . . . . .
$$ | . . X O X X . . . . .
$$ | . X X O O . . . . . .
$$ | . X O X . . . . . . .
$$ | . a O . . . . . . . .
$$ | . . . . . . . . . . .
$$ | . . . . . . . . . . .[/go]

Very cool!

_________________
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.

Yep that's it.