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
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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
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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.