I think white is unconditionally alive. Black's strongest attempt seems to be the following, but white can resist:

Click Here To Show Diagram Code

[go]$$B Status?
$$ . . . . . . . . . . . . .
$$ . . X X X X X X X X X . .
$$ . X . X O O X O O X . X .
$$ . . X O 2 1 O 4 . O X . .
$$ . . 5 O a 3 6 . b O . . .
$$ -------------------------[/go]

-- a and b are miai. If black plays 3 at 4, then white plays 4 at 3, sacrificing the two stones to live on the left.

I guess black might have stronger attempts that I have missed though. Playing on the point of symmetry does't seem to work - for example:

Click Here To Show Diagram Code

[go]$$B Status?
$$ . . . . . . . . . . . . .
$$ . . X X X X X X X X X . .
$$ . X . X O O X O O X . X .
$$ . . X O 6 3 O . 5 O X . .
$$ . . . O . 4 1 2 . O . . .
$$ -------------------------[/go]

It's a bit more complicated than it looks though. I await the SDKs and dan players to point out what I've missed

Hmm, I missed here until robinz pointed it out, and didn't understand why this could be considered a very difficult problem.

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . . . .
$$ . . X X X X X X X X X . .
$$ . X . X O O X O O X . X .
$$ . . X O 2 1 O 4 . O X . .
$$ . . . O . 3 . . . O . . .
$$ -------------------------[/go]

However, I still think there is a solution that kills white:

Click Here To Show Diagram Code

[go]$$B
$$ . . . . . . . . . . . . .
$$ . . X X X X X X X X X . .
$$ . X . X O O X O O X . X .
$$ . . X O O X O O . O X . .
$$ . . . O . X 6 . 5 O 7 . .
$$ -------------------------[/go]

Thanks Dusk Eagle - I think you're right. I always miss shortage of liberties issues like that when reading several moves in.

And I'd overlooked that move 4 for a long time too - when I started that post it was going to be an explanation of how black could kill

Click Here To Show Diagram Code

[go]$$B All stones alive
$$ . . . . . . . . . . . . .
$$ . . X X X X X X X X X . .
$$ . X . X O O X O O X . X .
$$ . . X O . 2 O . . O X . .
$$ . . . O . . 1 . . O . . .
$$ -------------------------[/go]

I never said that this problem is going to be difficult.