The position below is adapted from a recent game of mine. White has just passed, so it is black's move. White could have played j15 as the dame were being filled to fix the bad aji of the 2 black stones inside white's area, but then he would have lost by 0.5 points (Japanese rules). But bad aji won't win the game for black, he must find a sequence that works against any white resistance. The stakes could not be higher!
Note that a ko can be assumed as a success for black, as he only needs to gain 1 point to win the game, and there were indeed threats on the rest of the board. I have studied this position extensively and I believe black can win, though it is possible I missed something. This is a hard problem, to solve it without playing it out I think you need to be a high dan. I will give a few hints below, and post my solution later.
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . . O X X . . . , . . . | $$ | . . X O . . . . . X O X . . . . . . . | $$ | . . X O . . . . . . O X . . . . . . . | $$ | . . X O . . . . O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . . O X X . . . , . . . | $$ | . . X O . . . . . X O X . . . . . . . | $$ | . . X O . . . . . . O X . . . . . . . | $$ | . . X O . . . . O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
Hints:
1) Add a second stone and sacrifice both. 2) That white has a dango rather than eye in the lower left is relevant. 3) You need to take your shoes off to count the snapbacks.
Re: Exciting problem to decide a game
Posted: Mon Dec 05, 2011 5:49 pm
by Magicwand
i looked at it for 3 min and can not find any... i will try later when i have more time.
Re: Exciting problem to decide a game
Posted: Mon Dec 05, 2011 6:12 pm
by Magicwand
are you sure that there is answer to this question??? i spent few more minute..and i dont see anything but aji.
Re: Exciting problem to decide a game
Posted: Mon Dec 05, 2011 7:41 pm
by Loons
I just see dead ends as well. Albeit, I will now look at the hints.
Quite boring:
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . . O X X . . . , . . . | $$ | . . X O . . 7 5 3 X O X . . . . . . . | $$ | . . X O . . 6 4 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . 5 O X X . . . , . . . | $$ | . . X O . . . 3 4 X O X . . . . . . . | $$ | . . X O . . . . 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
...Guess I was nowhere close
Re: Exciting problem to decide a game
Posted: Mon Dec 05, 2011 7:57 pm
by cyclops
Without using the hint after a few minutes this 7kyu came up with:
$$Bc $$ +----------------------------- $$ | . . . . X O . . . O X . . . $$ | . . . . X O 8 . . O X . . . $$ | . . X X X O 7 . . O X . . . $$ | . . X O O 3 4 . . O X X . . $$ | . . X O . 5 . 2 . X O X . . $$ | . . X O . 6 1 . . . O X . . $$ | . . X O . . . . O O O X . . $$ | . X X O . 9 0 X O X X X . . $$ | . X O O . O O O X X . . . . $$ | . X O O O X X X . , . . . . $$ | . X O O O X . . . . . . . . $$ | . X X X X X . . . . . . . . $$ | . . . . . . . . . . . . . .
[go]$$Bc $$ +----------------------------- $$ | . . . . X O . . . O X . . . $$ | . . . . X O 8 . . O X . . . $$ | . . X X X O 7 . . O X . . . $$ | . . X O O 3 4 . . O X X . . $$ | . . X O . 5 . 2 . X O X . . $$ | . . X O . 6 1 . . . O X . . $$ | . . X O . . . . O O O X . . $$ | . X X O . 9 0 X O X X X . . $$ | . X O O . O O O X X . . . . $$ | . X O O O X X X . , . . . . $$ | . X O O O X . . . . . . . . $$ | . X X X X X . . . . . . . . $$ | . . . . . . . . . . . . . .[/go]
$$Bc $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O O . . O X . . $$ | . . X X X O X . . O X . . $$ | . . X O O X O 4 . O X X . $$ | . . X O . X 3 O . X O X . $$ | . . X O 7 O X . 2 . O X . $$ | . . X O . . 5 1 O O O X . $$ | . X X O . X O X O X X X . $$ | . X O O 6 O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .
[go]$$Bc $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O O . . O X . . $$ | . . X X X O X . . O X . . $$ | . . X O O X O 4 . O X X . $$ | . . X O . X 3 O . X O X . $$ | . . X O 7 O X . 2 . O X . $$ | . . X O . . 5 1 O O O X . $$ | . X X O . X O X O X X X . $$ | . X O O 6 O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]
edit: In the next post MagicWand exposes my mistake quite clearly. So skip my post please.
Re: Exciting problem to decide a game
Posted: Mon Dec 05, 2011 8:03 pm
by Magicwand
cyclops wrote:Without using the hint after a few minutes this 7kyu came up with:
$$Bc $$ +----------------------------- $$ | . . . . X O . . . O X . . . $$ | . . . . X O 8 . . O X . . . $$ | . . X X X O 7 . . O X . . . $$ | . . X O O 3 4 . . O X X . . $$ | . . X O . 5 . 2 . X O X . . $$ | . . X O . 6 1 . . . O X . . $$ | . . X O . . . . O O O X . . $$ | . X X O . 9 0 X O X X X . . $$ | . X O O . O O O X X . . . . $$ | . X O O O X X X . , . . . . $$ | . X O O O X . . . . . . . . $$ | . X X X X X . . . . . . . . $$ | . . . . . . . . . . . . . .
[go]$$Bc $$ +----------------------------- $$ | . . . . X O . . . O X . . . $$ | . . . . X O 8 . . O X . . . $$ | . . X X X O 7 . . O X . . . $$ | . . X O O 3 4 . . O X X . . $$ | . . X O . 5 . 2 . X O X . . $$ | . . X O . 6 1 . . . O X . . $$ | . . X O . . . . O O O X . . $$ | . X X O . 9 0 X O X X X . . $$ | . X O O . O O O X X . . . . $$ | . X O O O X X X . , . . . . $$ | . X O O O X . . . . . . . . $$ | . X X X X X . . . . . . . . $$ | . . . . . . . . . . . . . .[/go]
$$Bc $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O O . . O X . . $$ | . . X X X O X . . O X . . $$ | . . X O O X O 4 . O X X . $$ | . . X O . X 3 O . X O X . $$ | . . X O 7 O X . 2 . O X . $$ | . . X O . . 5 1 O O O X . $$ | . X X O . X O X O X X X . $$ | . X O O 6 O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .
[go]$$Bc $$ +--------------------------- $$ | . . . . X O . . . O X . . $$ | . . . . X O O . . O X . . $$ | . . X X X O X . . O X . . $$ | . . X O O X O 4 . O X X . $$ | . . X O . X 3 O . X O X . $$ | . . X O 7 O X . 2 . O X . $$ | . . X O . . 5 1 O O O X . $$ | . X X O . X O X O X X X . $$ | . X O O 6 O O O X X . . . $$ | . X O O O X X X . , . . . $$ | . X O O O X . . . . . . . $$ | . X X X X X . . . . . . . $$ | . . . . . . . . . . . . .[/go]
i think your 1 wont work
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . . O X X . . . , . . . | $$ | . . X O . . . . . X O X . . . . . . . | $$ | . . X O . . 1 . . . O X . . . . . . . | $$ | . . X O . . 2 . O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . 5 O X X . . . , . . . | $$ | . . X O . . . 3 4 X O X . . . . . . . | $$ | . . X O . . . . 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
I think Black wants to play in this order. If , Black will play instead of "a". What now? White does not seem able to escape without allowing Black to peep with "b" and cut off the three White stones. For example if , Black drives down and then plays "b" after White connects. This makes miai of "c" and "d".
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . 9 O X . . . . . . . . | $$ | . . . . X O . . 7 O X . . . . . . . . | $$ | . . X X X O . . 5 O X . . . . . . . . | $$ | . . X O O c b . 3 O X X . . . , . . . | $$ | . . X O . . . a 4 X O X . . . . . . . | $$ | . . X O . . 6 d 2 8 O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . 5 O X X . . . , . . . | $$ | . . X O . . . 3 4 X O X . . . . . . . | $$ | . . X O . . . . 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
I think Black wants to play in this order. If , Black will play instead of "a". What now? White does not seem able to escape without allowing Black to peep with "b" and cut off the three White stones. For example if , Black drives down and then plays "b" after White connects. This makes miai of "c" and "d".
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . 9 O X . . . . . . . . | $$ | . . . . X O . . 7 O X . . . . . . . . | $$ | . . X X X O . . 5 O X . . . . . . . . | $$ | . . X O O c b . 3 O X X . . . , . . . | $$ | . . X O . . . a 4 X O X . . . . . . . | $$ | . . X O . . 6 d 2 8 O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . 5 O X X . . . , . . . | $$ | . . X O . . . 3 4 X O X . . . . . . . | $$ | . . X O . . . . 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
I think Black wants to play in this order. If , Black will play instead of "a". What now? White does not seem able to escape without allowing Black to peep with "b" and cut off the three White stones. For example if , Black drives down and then plays "b" after White connects. This makes miai of "c" and "d".
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . 9 O X . . . . . . . . | $$ | . . . . X O . . 7 O X . . . . . . . . | $$ | . . X X X O . . 5 O X . . . . . . . . | $$ | . . X O O c b . 3 O X X . . . , . . . | $$ | . . X O . . . a 4 X O X . . . . . . . | $$ | . . X O . . 6 d 2 8 O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
[go]$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . . . X O . . . O X . . . . . . . . | $$ | . . X X X O . . . O X . . . . . . . . | $$ | . . X O O . . . 5 O X X . . . , . . . | $$ | . . X O . . . 3 4 X O X . . . . . . . | $$ | . . X O . . . . 2 . O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]
I think Black wants to play in this order. If , Black will play instead of "a". What now? White does not seem able to escape without allowing Black to peep with "b" and cut off the three White stones. For example if , Black drives down and then plays "b" after White connects. This makes miai of "c" and "d".
$$c Black to play $$ --------------------------------------- $$ | . . . . X O . . 9 O X . . . . . . . . | $$ | . . . . X O . . 7 O X . . . . . . . . | $$ | . . X X X O . . 5 O X . . . . . . . . | $$ | . . X O O c b . 3 O X X . . . , . . . | $$ | . . X O . . . a 4 X O X . . . . . . . | $$ | . . X O . . 6 d 2 8 O X . . . . . . . | $$ | . . X O . . . 1 O O O X . . . . . . . | $$ | . X X O . . . X O X X X . . . . . . . | $$ | . X O O . O O O X X . . . . . . . . . | $$ | . X O O O X X X . , . . . . . , . . . | $$ | . X O O O X . . . . . . . . . . . . . | $$ | . X X X X X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------
to H14 
in this order. If 
instead of "a". What now? White does not seem able to escape without allowing Black to peep with "b" and cut off the three White stones. For example if 
, Black drives down and then plays "b" after White connects. This makes miai of "c" and "d".
and 
, 
makes miai of "a" and "b" (Black has the atari at "c" if White connects against "b").