Solution by lavalyn 17k:
Black takes the corner for eye space. Now the best White can do is to minimize the eye space available, but the available space is sufficient to ensure life.
For your viewing pleasure, some failure diagrams:
Black, in his attempt to take more of the side, loses after and
: on the second line, six die but eight live.
What's wrong with white trying here?
It seems that black must ultimately play to the right of , but he cannot avoid filling in his own eye:
and black dies as before. How can black respond?
--satyreyes, unknown rank but probably very, very low
rokirovka: As a beginner, I find it helpful to show the shortest variation that proves the black group is alive. threatens to create two eyes in the corner. White plays
to reduce Black to one eye in the corner. But now Black plays
capturing
and
. After
, Black plays
at
, creating a second eye at
, and the black group has two eyes and lives. If White plays
at
, Black plays
at
and lives.
Also, I find it helpful to show the shortest route to life for Black if White plays at . Black cannot play on the first line immediately: If
at
,
at
reduces Black to one eye in the corner, and if
at
,
at
takes away the point Black needed for his second eye. So Black extends along the second line with
, threatening to play next at
, which would guarantee unconditional life in the corner with a straight five. So
is the only try to kill Black. Then Black extends again with
, again threatening to play next at
with a straight six and certain life. So
is the only try to kill. Now Black can finally play on the first line:
threatens to play at
and make two eyes in the corner.
reduces Black to one eye in the corner, but now
captures
and
. After
,
at
makes a second eye and Black lives. If White plays
at
,
at
also makes a second eye and lives.
So it seems to me that if White had a stone at in the original diagram,
would kill. White could then play
at
, and Black is dead with only one eye in the corner.
Elgoran?, 16k: Actually, Black can and will play after
. Playing
just gives Black another prisoner because of
. If White a, Black b and vice versa.
For your further viewing pleasure, some not so minor changes to the problem (by Sergio) :
If the stone is on the second line (instead of the third) Black is dead...
But what should White play in answer to a ?
Even if it's not a clear move to beginners is the only one that kills.
Deebster: Doesn't b kill Black too?
unkx80: Yes, b kills too.
If Black attempts to capture with , White plays
to prevent an eye at
. If Black captures at
, White plays at
, the vital point of the remaining straight three.
But what if Black plays ? White plays
to take away the last chance for an eye. Capture
any time to kill the group.
So we can conclude that in the original problem, Black's threat of escape along the second row is necessary for survival. With present, that threat disappears, and White can hane with impunity.