Building a live group on a quarter board where two sides are already black

Question

This exercise is kind of go club folklore: Given a quarter go board where two sides are already occupied by black (and unconditionally alive), white starts playing. White wins when she is able to create a living group in the quarter board.

$$ | X X X X X X X X X X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ ---------------------

It is also part of go club folklore that with correct play this task is impossible for white and black kills any white group.

What is known (or published) about this special fun exercise? Is the best solution already known?

For clarification: Here is an example of white trying to live (and fail):

$$ | X X X X X X X X X X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . . . . . . . . . X
$$ | . 1 3 . . . . . . X
$$ | . 2 4 W . . . . . X
$$ | . . . 6 5 . . . . X
$$ | . 7 . . . . . . . X
$$ ---------------------

White starts on the (3,4) point but black counters at (4,2). After the enclosure, the corner has only one eye, and Black's outer stones cannot be captured because of the outer walls helping them. Note that in this setup all ladders are favouring Black.

Answer 1

This has been discussed a lot in Sensei's Library (http://senseis.xmp.net/?BiggestCorner and http://senseis.xmp.net/?10x10CornerGame1). The consensus seems to be that white dies with 8 free spaces, but can live with 9 free spaces using 3-3 point and some clever tesujis. I copied some variations from Sensei's to EidoGo for easier studying: http://eidogo.com/#1ZUwMVRaH

Answer 2

I'm not familiar with this as folklore, but the setup is similar to the setup a person might use to work on corner problems. I believe that this could be answered by looking a many examples of corner joseki. Assuming white's goal here is simply to live, the border formed by black is too far removed from the corner to have a significant effect of white's play. The space enclosed by black may be intimidating, but most corner joseki is contained in a much smaller space.

See Sensei's Library for more examples, but I'll provide one here. Two note: I'm choosing one that I'm familiar with rather than a "best" example and white goes first in this because that's what you stipulated in your question.

W(3, 4) B(5, 4) W(5, 3) B(6, 3) W(4, 3) B(6, 3) W (3, 6) B(5, 7)

Now, given the black border of stones, black may play move 6 (5, 7) differently than the standard joseki. However, I believe that white's moves before that to provide a sufficiently strong foundation that black would lose the fight, or have to run back allowing white to take up more territory in the corner.