Unsolved Problems in Go

SmoothOper · Post by **SmoothOper** » Sat Nov 03, 2012 5:17 pm

I wonder if there are any unsolved problems in Go. Like Life and Death problems where the status is unknown.

hyperpape · Post by **hyperpape** » Sat Nov 03, 2012 5:43 pm

Yes. Of course.

See also: senseis.xmp.net/?IgoHatsuyoron

logan · Post by **logan** » Sat Nov 03, 2012 5:44 pm

The game of go is unsolved. That's the first response you'll most likely receive.

After this, I believe many of the classic problem collections didn't originally include answers so were later solved and written down by dedicated players in later editions of these classics. IIRC the most famous one is Igo Hatsuyoron problem #120 :

Click Here To Show Diagram Code: [go]$$B Black to play $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . O X . | $$ | . . . . . . . X O O . X O . . . . O . | $$ | . . . . . X . O . . . X . . . . O . . | $$ | . X O , . . . . . O . X . O O , . . . | $$ | . . X X . X . . . . O X X . X X O O . | $$ | . X . O . O . . . . . . X . X O . . . | $$ | . O O O . . O O . . O O . O X . . . . | $$ | O . . X . . . . . . . . . . X X X X X | $$ | . . . X . . . O . . O . X X X X . O O | $$ | X O O , . X . . . O . X . O O O O . . | $$ | X . . O X . . . . O . X . . O . . X X | $$ | X . . O X . . . X O . . . . . X X O O | $$ | X X . . X . . O . O . . . . . . X X O | $$ | . O O X O X . . . O . . X . O . . O O | $$ | . . X . . X . . . . X . . . X . O O O | $$ | O X X , X . . O . , O O O . O X O . X | $$ | . . . . O X . . . . . . . . . X X O X | $$ | O . X . . . . . O . . . O X O X . . . | $$ | . X . . . . . . . . . . O X X X . . . | $$ ---------------------------------------[/go]

I think a new western book just came out early this year about the problem, but I don't know if it's considered definitively solved now.

Other than this, you can also ponder over the many problems that editors dropped from later editions of classics because they were 'found not to work.' Maybe there's something to be found in those. The Guanzi Pu usually receives a high amount of editing whenever a new version is published.

Also, you can consider positions where the status changes depending on ruleset. Perhaps these perplexed people in the past (though for slightly difference reasons).

TheBigH · Post by **TheBigH** » Sat Nov 03, 2012 6:10 pm

logan wrote:I think a new western book just came out early this year about the problem, but I don't know if it's considered definitively solved now.

This is what you want.

RobertJasiek · Post by **RobertJasiek** » Sat Nov 03, 2012 9:55 pm

Countless of go theory research questions are unresolved.

Cassandra · Post by **Cassandra** » Sun Nov 04, 2012 1:43 am

logan wrote:I think a new western book just came out early this year about the problem, but I don't know if it's considered definitively solved now.

I don't know your definition of "is considered definitely solved".

Indeed, there are two challenges that refer to "definitely" and "considered by whom".

We do not know any professional publication that includes the all-decisive Guzumi in the top right corner, leading to a Black win.

The latest professional publication (on Igo Hatsuyoron in total), by Cheng Xiaoliu 6p in 2010, now includes several moves that we found earlier, and used in our solution for problem #120. However, the solution given by Cheng, ending with Jigo, is not correct, because he missed another valuable move for White, a Tsuke in the upper left corner, found by Yamada Shinji 6p, giving White a win by two points. We do not think that Dosetsu created a problem "Black to play and lose by the smallest possible margin."

It is extremely difficult to get professionals involved into the problem, because it is so very complex and difficult.

However, we got very valuable feedback from professor Jeong SooHyun 9p from Myongji University in Seoul, including a statement that there were no grave mistakes in our solution.

cyclops · Post by **cyclops** » Mon Nov 12, 2012 6:56 am

I wonder if there are any unsolvable problems in Go. Would be nice.

Li Kao · Post by **Li Kao** » Mon Nov 12, 2012 7:08 am

What do you mean by "unsolvable"? That the given task is impossible to fulfill?

cyclops · Post by **cyclops** » Mon Nov 12, 2012 8:38 am

To find a consistent set of axioms for all mathematics is an unsolvable problem. ( see [url="http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems"]Gödel[/url] ). Likewise there might be unsolvable problems in go. But what should be considered as valid problem in Go? For example "get RJ and MW to agree" I wouldn't consider as a go problem .

RobertJasiek · Post by **RobertJasiek** » Mon Nov 12, 2012 9:14 am

One of the unsolvable because undecidable problems you find here:

http://home.snafu.de/jasiek/mistakes.html

HermanHiddema · Post by **HermanHiddema** » Mon Nov 12, 2012 11:32 am

RobertJasiek wrote:One of the unsolvable because undecidable problems you find here:

http://home.snafu.de/jasiek/mistakes.html

Seems to me that this does not qualify, as the distinction between a "no result" and a tie is irrelevant when both are better than losing (and worse than winning).

RobertJasiek · Post by **RobertJasiek** » Mon Nov 12, 2012 12:10 pm

HermanHiddema wrote:when both are better than losing (and worse than winning).

Such a condition could be overriding indeed. Suitable global conditions are needed for a decision between tie and no result to become relevant.

HermanHiddema · Post by **HermanHiddema** » Mon Nov 12, 2012 3:13 pm

RobertJasiek wrote:
HermanHiddema wrote:when both are better than losing (and worse than winning).

Such a condition could be overriding indeed. Suitable global conditions are needed for a decision between tie and no result to become relevant.

And as soon as the global conditions are known, the choice is no longer undecidable. If we take as a given that the global conditions for any game are known, then the problem is never undecidable. (And if we don't, then every position becomes undecidable, I guess).

TheBigH · Post by **TheBigH** » Mon Nov 12, 2012 3:51 pm

It seems to me that this is just an issue of insufficient information. I mean, there are two easily identifiable potential solutions. The preferred one depends on information that hasn't been given (ie. whether a jigo is better than a no result), but that doesn't mean the problem is undecidable. That would be like saying the equation x²=1 is undecidable because both x = 1 and x = -1 are solutions, which is of course ridiculous.

NoSkill · Post by **NoSkill** » Mon Nov 12, 2012 5:49 pm

Any unsolved problem is only because it is impossible to solve (IE black to kill white when white has two eyes) or the problem is too open ended (IE that igohatsu book having a 100+ move variation, cant be sure of answer).

Any problem that has been looked at by 9p and not solved is not worth solving, and probably has no right answer.

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