Sunday Problem #28

Published 13 Dec 2020 by antti (last edited 27 Dec 2020)

Sometimes it is good to spend time and effort trying to solve difficult problems. Even if you are unable to find the solution, this will improve your reading and, more importantly, help build character in a way that you will get less demotivated by difficult game positions.

This problem was first shown to me by ‘Bass’, a Finnish go player, more than ten years ago; he liked to call it the Aivovamma, or ‘Brain damage’ problem. Don’t expect to solve it in five minutes.

Black to play.

Black is unable to save her two stones, as shown in this diagram. Up to 4, four black stones cannot avoid getting captured, and the white group will get two eyes.
The lower-side white group is in fact unconditionally alive, and so the best Black can do is get her own group to live.
Solution (1)
The eye-removing move of 1 is Black’s strongest move. After this, we have an interesting subproblem of how White can possibly live; the sequence of 2–8, aiming to utilise an under-the-stones tesuji, is the solution.
If instead of 4 White plays 5, Black plays 4, and the white group will simply die.
Alternatively, if instead of 6 White plays 7, Black plays 6 and White ends up with a large eye in a capturing race. However, the outer black group has more liberties, and so this would also lead to White’s getting captured.
Solution (2)
After White captures four black stones, the black cut of 9 may seem severe at first, but white 10 sets up the under-the-stones tesuji for two eyes.
Solution (3)
The moves 12–14 follow and, while the white lower-side group lives, Black at least gets one eye in sente. The question is then, where Black can create a second eye.
Black 15 looks promising, but White unleashes a severe attack with 16. In the most local sense, white 16 would deprive Black of her eye, but the surrounding shape in this problem is a bit special.
After 17–22 get played, Black unleashes her final tesuji of 23. After this, White cannot prevent Black from forming her second eye; for example, white 24 fails to 25–27. Finally, Black lives.

Comments (2)

antti wrote 4 months, 1 week ago:

Solution added. Congratulations if you got this right!

sig wrote 4 months, 1 week ago:

Well, I got the first move right :)