byorgey 15k:
I'll give it a try. (= This is indeed a cool problem.
is the proper solution.
If white plays at any of the three points marked a, black captures at b, making the second eye, and the remaining two a points are miai to connect the eyes.
If white plays instead, black must capture with
. Black then captures the throw-in at
and a and b are miai.
Some failed attempts:
After there is no way for black to make a second eye.
at
fails in similar fashion.
After ,
takes away the second eye. Playing
at a does not help; black can capture
but still does not get a second eye. Playing
at b does not help either since white has enough time to escape.
does not work either: after the exchange of
and
, the throw-in at
dashes black's hopes for a second eye.