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July 2001's Go Answer of the Month

Dia 1 - Status?

Dia 1

This problem has a large number of twists and turns in it. Every time I think I have the answer, I manage to find a variant which refutes my previous solution. This variant of the solution was sent to me by Tim Hunt who pointed out a flaw in my original Dia 9. With this Feb 2002 change, Dias 10 onwards have been removed. Then in May 2002, John Carian pointed out that my text didn't match the diagrams and Dia 7 was the "right" answer.

I shall present "answers" in roughly the order I discovered them, each refuting the previous one!

Initial thoughts

White can kill - he plays at the 2-2 point, captures 3 stones and can then easily prevent Black making two eyes. This at least doesn't change through the rest of the solution(s), so the problem is really "Black to play and ...".

Black to play. If he lets White capture the 3 stones he dies, so he must protect the cut at the 2-2 point. Candidates. for this are the 2-2 point, the top 2-1 point and the left 2-1 point. Start with the direct connection.

Dia 2 - The direct connection

Dia 2

After 4, the 'A's are miai for an eye in the corner and the 'B's for no eye on the upper edge, so Black has only one eye and is dead.

Dia 3 - The top 2-1 point

Dia 3

White 2 forces 3 else the 3 stones get captured leaving Black too small a space to live at the top. By 8, Black has only 1 eye and is again dead.

Dia 4 - The left 2-1 point

Dia 4

This doesn't look like a good move, but as it does protect the cutting point, we'd better try it.

Black 1 forces 2 to prevent two eyes in the corner. That leaves the now four stones on the left vulnerable, so protect them with Black 3 but then White 4 reduces the upper side to no eyes so again Black dies.

Status: Black is dead.

But then Black thinks "maybe I can let the four stones go - is this an 'under-the-stones' situation?".

Dia 5 & 6 - Under the stones

Dia 5   Dia 6

Yes it is. White 6 captures four stones, but 7 sets up the recapture of the three white stones for one eye (at the 1-1 point) after 9, even if White throws in with 10 etc. There is obviously one eye on the upper side.

Dia 7 - White makes the best of a bad job

Dia 7

Realising what is happening, White plays 2 in Dia 7 instead to let Black live a small life in the corner and to take some profit capturing the stones at the top.

Status: Black is alive (small). White has some profit.

Further thought by Black persuades him that he can live larger...

Dia 8 - A bigger Black life.

Dia 8

Black connects his group first and then lives. Much better.

Dia 9 - White can stop this larger life.

Dia 9 7 at 2.

Originally I had White 10' on the 1-1 point and Black living. It has been pointed out to me that 10 here is better for White – because Black dies with just the one eye in the corner. And this prevents the mass of other variants I reviewed in following diagrams.

(If you are having difficulty visualising the situation after Dia 9, Black 11 cannot make an eye on the upper edge due to liberty shortage. If Black 11 is used to capture White 4 & 8 then White 12 extends from White 10 to prevent the upper edge eye.

Therefore Black doesn't have a bigger life.

For the record, Go Tools reckons that If Black 7' is played next to 10 and Black can win the ko twice he can live. This seems too much to aim for practically.

So the real answer is
Status: Black has a small life in the corner (Dia 7).

Unless you know different...

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