The really most difficult problem ever

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Cassandra
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The really most difficult problem ever

Post by Cassandra »

Everybody, who wants to discuss details of Igo Hatsuyoron's unsolved problem 120, is envited to do it here.



You may want to refer to

http://senseis.xmp.net/?MostDifficultProblemEver

or

http://www.dgob.de/dgoz/trmdpe/index.htm#E
Last edited by Cassandra on Sat May 01, 2010 1:30 am, edited 1 time in total.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: The really most difficult problem ever

Post by Solomon »

Yeah, don't think anyone who's never seen it before can solve it when Fujisawa Shuko himself required student assistance to solve it :-?.

Also, relevant: http://www.emptytriangle.com/archive/show/29
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Re: The really most difficult problem ever

Post by Cassandra »

Araban wrote:Yeah, don't think anyone who's never seen it before can solve it when Fujisawa Shuko himself required student assistance to solve it :-?.

Be aware that the sequence published in Go World #29 (developed by Fujisawa Shuko and his students) does not give the best result for Black and - what is more important - does NOT really solve the problem (if the task should be "... and win"), because professionals overlooked a White opportunity.

So I think that there could be many details - even concerning the known professional sequences - worth discussing.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: The really most difficult problem ever

Post by Cassandra »

I'm in fear that the whole problem is a little complex. ;-)

From time to time I'll post some local problems, concerning sequences I encountered during my investigations. And I'm absolutely not sure to know the answers already.

Below you will find the first one.



Does a Black move at A capture the lower left quadrant of the board ?
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: The really most difficult problem ever

Post by Cassandra »

The fourth edition of my supplement is online, containing over 1,000 variations after "my" Guzumi in the top right corner, which might win the problem for Black.

You will find it at:

http://www.dgob.de/dgoz/trmdpe/newweb3/htm/0000.htm
Last edited by Cassandra on Sat Feb 19, 2011 9:14 am, edited 1 time in total.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: The really most difficult problem ever

Post by Numsgil »

What makes it a problem and not just an unfinished game? It's presumably in the end game, so there's presumably only one optimal path? But how do you know you've solved it then, since it relies so heavily on reading out white's responses?
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Re: The really most difficult problem ever

Post by Li Kao »

Numsgil wrote:What makes it a problem and not just an unfinished game? It's presumably in the end game, so there's presumably only one optimal path? But how do you know you've solved it then, since it relies so heavily on reading out white's responses?

Or even how do you know it has a solution?
Sanity is for the weak.
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Re: The really most difficult problem ever

Post by amnal »

Numsgil wrote:What makes it a problem and not just an unfinished game? It's presumably in the end game, so there's presumably only one optimal path? But how do you know you've solved it then, since it relies so heavily on reading out white's responses?


It really is a problem, not an unfinished game, though whether it has a solution is more debatable. The stone placement is fairly contrived (these shapes wouldn't occur in an actual game), and it's complex because the main necessary reading sequences are vastly long and complex with many important variations.
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Re: The really most difficult problem ever

Post by Harleqin »

The starting position of the problem is here:

http://www.dgob.de/dgoz/trmdpe/hauptpfad/index.htm

You can clearly see that it is a constructed problem and not just an arbitrary unfinished game. It has a main theme and a lot of details.
A good system naturally covers all corner cases without further effort.
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Re: The really most difficult problem ever

Post by Cassandra »

Harleqin wrote:The starting position of the problem is here:

http://www.dgob.de/dgoz/trmdpe/hauptpfad/index.htm

You can clearly see that it is a constructed problem and not just an arbitrary unfinished game. It has a main theme and a lot of details.

The starting point for the English version is:

http://www.dgob.de/dgoz/trmdpe/mainpath/index.htm

White has 71 stones on the board, Black only 70. To make the position "game-like" (it's Black's turn), one has to assume that Black lost a stone, what could have "happened" in the lower right. But this would turn a final result of "Black + 1" to "Jigo".


amnal wrote:The stone placement is fairly contrived (these shapes wouldn't occur in an actual game), and it's complex because the main necessary reading sequences are vastly long and complex with many important variations.

The placement of the stones is as brilliant as the problem itself. It seems impossible to either add a stone or take one stone away without destroying the flow of the decisive sequences.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Re: The really most difficult problem ever

Post by Cassandra »

Let me give you a short introduction into what three amateurs think might be the solution of Igo Hatsuyoron's problem #120.

I will not explain the standard moves of the "classical" solution, provided by Fujisawa Shuko 9p in 1982, in detail here. If you are interested in, please refer to http://www.dgob.de/dgoz/trmdpe/mainpath/03/index.htm, for example.

If you want to go through these sequences using EidoGo, please refer to the next posting. I've used diagrams here because these might be simpler to quote.

Click Here To Show Diagram Code
[go]$$B 1-10
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 . . |
$$ | X . . O X . . . . O . X . . O . 3 X X |
$$ | X . . O X . . . X O . 5 4 . . X X O O |
$$ | X X . . X . . O . O . 7 6 . . . X X O |
$$ | . O O X O X . . . O . . X 8 O . . O O |
$$ | . . X . . X . . . . X . 0 9 X 1 O O O |
$$ | 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 . 2 . |
$$ | . X . . . . . . . . . . O X X X . . . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm11 11-20
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 9 O O O O . . |
$$ | X . . O X . . . . O . X a 0 O . X X X |
$$ | X . . O X . . . X O . X O 6 5 X X O O |
$$ | X X . . X . . O . O . X O 7 8 . X X O |
$$ | . O O X O X . . . O . 1 X O O 2 3 O O |
$$ | . . X . . X . . . . X . O X X X O O O |
$$ | O X X , X . . O . , O O O . O X O 4 X |
$$ | . . . . O X . . . . . . . . . X X O X |
$$ | O . X . . . . . O . . . O X O X . O . |
$$ | . X . . . . . . . . . . O X X X . . . |
$$ ---------------------------------------[/go]


We are unsure whether Black 19 might be played at 20 (= the second Throw-in, followed by W a - B 19 - W 20). We were unable to find the Semeai, mentioned by Fujisawa Shuko 9p, ending futile for Black thereafter.

Click Here To Show Diagram Code
[go]$$Bm21 21-30
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 |
$$ | . . . X . . . O . . O . X X X X 2 O O |
$$ | X O O , . X . . . O . X X O O O O 1 . |
$$ | X . . O X . . . . O . X . O O . X X X |
$$ | X . . O X . . . X O . X O O X X X O O |
$$ | X X . . X . . O . O . X O . O . X X O |
$$ | . O O X O X . . . O . X X O O O X O O |
$$ | . . X . . X . . . . X . O X X X O O O |
$$ | O X X , X . . O . . O O O 3 O X O O X |
$$ | . . . . O X . . . . . 9 7 . 6 X X O X |
$$ | O . X . . . . . O . 0 8 O X O X . O 5 |
$$ | . X . . . . . . . . . . O X X X . 4 . |
$$ ---------------------------------------[/go]


As far as I know, the exchange Black 21 - White 22 is shown in the Chinese edition of Igo Hatsuyoron. It prevents a later exchange of White 21 - Black 22 with Black's stone at 22 ending as additional White's prisoner in the Semeai variation.

Click Here To Show Diagram Code
[go]$$Bm31 31-40
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 |
$$ | . . . X . . . O . . O . X X X X O O O |
$$ | X O O , . X . . . O . X X O O O O X . |
$$ | X . . O X . . . . O . X . O O . X X X |
$$ | X . . O X . . . X O . X O O X X X O O |
$$ | X X . . X . . O . O . X O . O . X X O |
$$ | . O O X O X . . . O . X X O O O X O O |
$$ | . . X . . X . . . 0 X . O X X X O O O |
$$ | O X X , X . . O 9 2 O O O X O X O O X |
$$ | . . . . O X . 6 5 3 1 X X . O X X O X |
$$ | O . X . . . 7 8 O 4 O O O X O X . O X |
$$ | . X . . . . . . . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm41 41-50
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 |
$$ | . . . X . . . O . . O . X X X X O O O |
$$ | X O O , . X . 0 9 O . X X O O O O X . |
$$ | X . . O X . . 8 7 O . X . O O . X X X |
$$ | X . . O X . . 6 X O . X O O X X X O O |
$$ | X X . . X . . O 5 O . X O . O . X X O |
$$ | . O O X O X . 4 3 O . X X O O O X O O |
$$ | . . X . . X . 2 1 O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | . . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . . . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm51 51-60
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . 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 . . . 8 . . X . X O . . . |
$$ | . O O O . . O O 9 7 O O . O X . . . . |
$$ | O . . X . . . 0 2 5 6 . . . X X X X X |
$$ | . . . X . . . O 1 3 O . X X X X O O O |
$$ | X O O , . X . O X O 4 X X O O O O X . |
$$ | X . . O X . . O X O . X . O O . X X X |
$$ | X . . O X . . O X O . X O O X X X O O |
$$ | X X . . X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O . X X O O O X O O |
$$ | . . X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | . . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . . . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm61 61-64
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . O X . |
$$ | . . . . . . . X O O . X O . . . . O . |
$$ | . . . . . X . O . . . X . . . . O . . |
$$ | . X O , . . . . . O . X . O O . . . . |
$$ | . . X X . X . 4 2 . O X X . X X O O . |
$$ | . X . O . O . 3 1 O . . X . X O . . . |
$$ | . O O O . . O O X X O O . O X . . . . |
$$ | O . . X . . . O O X O . . . X X X X X |
$$ | . . . X . . . O X X O . X X X X O O O |
$$ | X O O , . X . O X O O X X O O O O X . |
$$ | X . . O X . . O X O . X . O O . X X X |
$$ | X . . O X . . O X O . X O O X X X O O |
$$ | X X . . X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O . X X O O O X O O |
$$ | . . X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | . . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . . . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm65 65-74
$$ ---------------------------------------
$$ | . . . . . . . . . . . . 5 . . . O X . |
$$ | . . . . . . . X O O . X O 3 6 . . O . |
$$ | . . . . . X . O . . . X 4 . b 2 O . . |
$$ | . X O , . . . . . O . X . O O 1 . . . |
$$ | . . X X . X 0 O O . O X X . X X O O . |
$$ | . X . O . O 9 X X O . . X . X O a 8 . |
$$ | . O O O . . O O X X O O . O X . . 7 . |
$$ | O . . X . . . O O X O . . . X X X X X |
$$ | . . . X . . . O X X O . X X X X O O O |
$$ | X O O , . X . O X O O X X O O O O X . |
$$ | X . . O X . . O X O . X . O O . X X X |
$$ | X . . O X . . O X O . X O O X X X O O |
$$ | X X . . X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O . X X O O O X O O |
$$ | . . X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | . . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . . . . . . O X X X . O . |
$$ ---------------------------------------[/go]


We think that Black must reduce White's top right corner, starting with Black 65, and play the Guzumi of Black 71 before playing the Crosscut sequence in the centre, starting with Black 73. Black may choose the order of 71 - 65 - 67 - 69 for his moves in the top right.
Black 67 is the Hasami-Tsuke of Harry Fearnley and can only be played in conjunction with my Guzumi at 71. The two false Eyes at a and b provide Black's top right group with an additional external liberty, making it possible to connect his pivotal stones of 67 and 69 later.

Click Here To Show Diagram Code
[go]$$Bm75 75-84
$$ ---------------------------------------
$$ | . . . . . . . . . . . . X . . . O X . |
$$ | . . . . . . . X O O . X O X O . . O . |
$$ | . . . . . X . O . . . X O . . O O . . |
$$ | . X O , . . . . . O . X . O O X . . . |
$$ | . . X X 5 X O O O . O X X . X X O O . |
$$ | . X . O 2 O X X X O . . X . X O . O . |
$$ | . O O O . 1 O O X X O O . O X . . X . |
$$ | O . . X . 3 . O O X O . . . X X X X X |
$$ | . . . X . . . O X X O . X X X X O O O |
$$ | X O O , . X . O X O O X X O O O O X . |
$$ | X . . O X . . O X O . X . O O . X X X |
$$ | X . . O X . . O X O . X O O X X X O O |
$$ | X X 6 . X . . O X O . X O . O . X X O |
$$ | 7 O O X O X . O X O . X X O O O X O O |
$$ | 9 8 X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | 0 . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . 4 . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm85 85-92
$$ ---------------------------------------
$$ | . . . . . . . . . . . . X . . . O X . |
$$ | . . . . . . . X O O . X O X O . . O . |
$$ | . . . . . X . O . . . X O . . O O . . |
$$ | . X O , . . . . . O . X . O O X . . . |
$$ | . . X X X X O O O . O X X . X X O O . |
$$ | . X . O O O X X X O . . X . X O . O . |
$$ | 4 O O O . X O O X X O O . O X . . X . |
$$ | O 3 . X . X . O O X O . . . X X X X X |
$$ | 2 1 . X . . . O X X O . X X X X O O O |
$$ | X O O , . X . O X O O X X O O O O X . |
$$ | X 5 6 O X . . O X O . X . O O . X X X |
$$ | X 7 8 O X . . O X O . X O O X X X O O |
$$ | X X O . X . . O X O . X O . O . X X O |
$$ | X O O X O X . O X O . X X O O O X O O |
$$ | X O X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm93 93-102
$$ ---------------------------------------
$$ | . . . . . . . . . . . . X . 0 . O X . |
$$ | . . . . . . . X O O . X O X O . . O . |
$$ | . . . . . X . O . . . X O . . O O . . |
$$ | . X O , . . . . . O . X . O O X . . . |
$$ | . . X X X X O O O . O X X . X X O O . |
$$ | . X . O O O X X X O . . X . X O . O . |
$$ | O O O O . X O O X X O O 8 O X . . X . |
$$ | O X . X . X . O O X O . . . X X X X X |
$$ | O X . X . . . O X X O . X X X X O O O |
$$ | 2 O O , . X . O X O O X X O O O O X . |
$$ | 1 6 O O X . . O X O . X . O O . X X X |
$$ | 7 3 O O X . . O X O . X O O X X X O O |
$$ | 5 . O 9 X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O . X X O O O X O O |
$$ | 4 O X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm103 103-112
$$ ---------------------------------------
$$ | . . . . . . . . . . 6 3 X 1 O . O X . |
$$ | . . . . . . . X O O 4 X O X O . . O . |
$$ | . . . . . X . O . . 8 X O 2 . O O . . |
$$ | . X O , . . . . . O . X . O O X . . . |
$$ | . . X X X X O O O . O X X . X X O O . |
$$ | 9 X . O O O X X X O . 0 X . X O . O . |
$$ | O O O O 5 X O O X X O O O O X . . X . |
$$ | O X . X . X . O O X O . . . X X X X X |
$$ | O X . X . . . O X X O . X X X X O O O |
$$ | O O O 7 . X . O X O O X X O O O O X . |
$$ | X O O O X . . O X O . X . O O . X X X |
$$ | X X O O X . . O X O . X O O X X X O O |
$$ | X . O X X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O . X X O O O X O O |
$$ | O O X . . X . O X O X . O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O . . . O X . O X X X X X . O X X O X |
$$ | O . X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm113 113-122
$$ ---------------------------------------
$$ | . . . . . . . . . . O X X X O . O X . |
$$ | . . . . . . . X O O O X O X O . . O . |
$$ | . . . . . X . O . . O X O O . O O . . |
$$ | . X O , . . . . . O . X . O O X 8 . . |
$$ | . . X X X X O O O . O X X 2 X X O O . |
$$ | X X 1 O O O X X X O . O X 3 X O . O 0 |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X 5 X . X . O O X O . . . X X X X X |
$$ | O X 7 X . . . O X X O . X X X X O O O |
$$ | O O O X . X . O X O O X X O O O O X . |
$$ | X O O O X . . O X O . X . O O . X X X |
$$ | X X O O X . . O X O . X O O X X X O O |
$$ | X . O X X . . O X O . X O . O . X X O |
$$ | . O O X O X . O X O 4 X X O O O X O O |
$$ | O O X . . X . O X O X 6 O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O . . . O X . O X X X X X . O X X O X |
$$ | O 9 X . . . X O O O O O O X O X . O X |
$$ | . X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm123 123-128
$$ ---------------------------------------
$$ | . . . . . . . . . . O X X X O . O X . |
$$ | . . . . . . . X O O O X O X O . . O . |
$$ | . . . . . X . O . . O X O O . O O . . |
$$ | . X O , . . . . . O . X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . 4 . X X X X X |
$$ | O X X X . . . O X X O 2 X X X X O O O |
$$ | O O O X . X . O X O O X X O O O O X . |
$$ | X O O O X . . O X O . X . O O . X X X |
$$ | X X O O X . . O X O . X O O X X X O O |
$$ | X 5 O X X . . O X O . X O . O . X X O |
$$ | 6 O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O 1 . . O X . O X X X X X . O X X O X |
$$ | O X X . . . X O O O O O O X O X . O X |
$$ | 3 X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm129 129-136
$$ ---------------------------------------
$$ | . . . . . . . . . . O X X X O . O X . |
$$ | . . . . . . . X O O O X O X O . . O . |
$$ | . . . . . X . O . . O X O O . O O . . |
$$ | . X O , . . . . . O 2 X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . O 4 X X X X X |
$$ | O X X X . . . O X X O O X X X X O O O |
$$ | O O O X . X . O X O O X X O O O O X . |
$$ | 3 O O O X . . O X O 6 X . O O . X X X |
$$ | 1 5 O O X . . O X O . X O O X X X O O |
$$ | 7 8 O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O X . . O X . O X X X X X . O X X O X |
$$ | O X X . . . X O O O O O O X O X . O X |
$$ | X X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm137 137-146
$$ ---------------------------------------
$$ | . . . . . 7 . 8 . . O X X X O . O X . |
$$ | . . . . 3 2 4 X O O O X O X O . . O . |
$$ | . . . 9 6 X 5 O . . O X O O . O O . . |
$$ | . X O , . . . . . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . . . O X X O O X X X X O O O |
$$ | O O O X . X 0 O X O O X X O O O O X . |
$$ | . O O O X . . O X O O X . O O . X X X |
$$ | 1 . O O X . . O X O . X O O X X X O O |
$$ | . O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O X . . O X . O X X X X X . O X X O X |
$$ | O X X . . . X O O O O O O X O X . O X |
$$ | X X . . . . . O . . . . O X X X . O . |
$$ ---------------------------------------[/go]


White 138 is the Tsuke of Yamada Shinji 5p. It can be played even at this early moment, because White could capture Black's centre string in Sente at any time she likes. Black cannot resist with 139 at 140, because White would be able to reach a Seki in the top left corner thereafter.

Click Here To Show Diagram Code
[go]$$Bm147 147-156
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X O X X O . . O X O O . O O . . |
$$ | . X O , 9 . 7 8 . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . 1 . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | . O O O X . . O X O O X . O O . X X X |
$$ | X . O O X . . O X O . X O O X X X O O |
$$ | . O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X . . O X O O O O X O X O O X |
$$ | O X . . O X 0 O X X X X X . O X X O X |
$$ | O X X . 3 2 X O O O O O O X O X . O X |
$$ | X X . . 5 4 6 O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm157 157
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | . O O O X . . O X O O X . O O a X X X |
$$ | X . O O X . . O X O . X O O X X X O O |
$$ | . O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X 1 . O X O O O O X O X O O X |
$$ | O X . . O X O O X X X X X b O X X O X |
$$ | O X X . X O . O O O O O O X O X . O X |
$$ | X X . . X O O O . . . . O X X X . O . |
$$ ---------------------------------------[/go]


As ususal, the Endgame on the left can be finished first.
Now a is the correct choice for White.

Click Here To Show Diagram Code
[go]$$Wm158 158-161
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . 3 X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | . O O O X . . O X O O X 2 O O 1 X X X |
$$ | X . O O X . . O X O . X O O X X X O O |
$$ | . O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X X . O X O O O O X O X O O X |
$$ | O X . . O X O O X X X X X 4 O X X O X |
$$ | O X X . X O . O O O O O O X O X . O X |
$$ | X X . . X O O O . . . . O X X X . O . |
$$ ---------------------------------------[/go]


White continues the Semeai with 158.

Click Here To Show Diagram Code
[go]$$Wm162 162-166
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . O X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | 2 O O O X . . O X O O X X O O O X X X |
$$ | X 4 O O X . . O X O 3 X O O X X X O O |
$$ | 5 O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X X . O X O O O O X . X O O X |
$$ | O X . . O X O O X X X X X X 1 X X O X |
$$ | O X X . X O . O O O O O O X . X . O X |
$$ | X X . . X O O O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm167 167-174
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O 4 O O . . |
$$ | . X O , X . X O . O O X 6 O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . O X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | 3 O O O X . . O X O O X X O O O X X X |
$$ | 1 . O O X . . O X O O X O O X X X O O |
$$ | O O O X X . . O X O 2 X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X X . O X O O O O X . X O O X |
$$ | O X . . O X O O X X X X X X O X X O X |
$$ | O X X . X O . O O O O O O X . X 5 O X |
$$ | X X . . X O O O . . . . O X X X 7 O 8 |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm175 175-179
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O O O O . . |
$$ | . X O , X . X O . O O X O O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X 4 O X 2 |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | X O O O X . . O X O O X X O O O X X X |
$$ | X . O O X . . O X O O X O O X X X O O |
$$ | O O O X X . . O X O O X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X X . O X O O O O X . X O O 3 |
$$ | O X . . O X O O X X X X X X O X X O 1 |
$$ | O X X . X O . O O O O O O X . X X O 5 |
$$ | X X . . X O O O . . . . O X X X X O O |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$ The End
$$ ---------------------------------------
$$ | . . . . . X . O . . O . . . O . O X . |
$$ | . . . . X O O . O O O . O . O . . O . |
$$ | . . . X . X X O . . O . O O O O O . . |
$$ | . X O , X . X O . O O . O O O , O . . |
$$ | . . X X X X O O O . O . . O . . O O . |
$$ | X X X O O O X X X O . O . . . O . O O |
$$ | O O O O X X O O X X O O O O . O O . O |
$$ | O X X X . X . O O X O . O O . . . . . |
$$ | O X X X . X . O X X O O . . . . O O O |
$$ | O O O X . X O O X O O . . O O O O X . |
$$ | X O O O X . . O X O O . . O O O X X X |
$$ | X . O O X . . O X O O . O O X X X . . |
$$ | O O O X X . . O X O O . O . O . X X . |
$$ | O O O X O X . O X O O . . O O O X . . |
$$ | O O X . . X . O X O . O O X X X . . . |
$$ | O X X , X X . O X O O O O X . X . . X |
$$ | O X . . O X O O X X X X X X O X X . X |
$$ | O X X . X O . O O O O O O X . X X . X |
$$ | X X . . X O O O . . . . O X X X X . . |
$$ ---------------------------------------[/go]


Black has 77 points of territory + 50 prisoners = 127 points in total.
White has 62 points of territory + 63 prisoners = 125 points in total.

Black wins be 2 points.

The problem's setup contains 71 White stones, but only 70 Black stones. If we assume that a 71th Black stone at T6 got captured beforehand, the score would be Black + 1.

White has captured Black's group in the top right, so none of Black's "reducing" moves there - because answered by a White one - do matter here. These reducing moves are necessary to prevent White from choosing the Capture variation, shown below.


+ + + + + + + + + + + + + + + + + + + +


Click Here To Show Diagram Code
[go]$$Wm158 158
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O X X X O . O X X X O . O O |
$$ | O O O O X X O O X X O O O O X . . X . |
$$ | O X X X . X . O O X O . O O X X X X X |
$$ | O X X X . X . O X X O O X X X X O O O |
$$ | O O O X . X O O X O O X X O O O O X . |
$$ | . O O O X . . O X O O X . O O . X X X |
$$ | X . O O X . . O X O . X O O X X X O O |
$$ | . O O X X . . O X O . X O . O . X X O |
$$ | O O O X O X . O X O O X X O O O X O O |
$$ | O O X . . X . O X O . O O X X X O O O |
$$ | O X X , X X . O X O O O O X O X O O X |
$$ | O X . . O X O O X X X X X 1 O X X O X |
$$ | O X X . X O . O O O O O O X O X . O X |
$$ | X X . . X O O O . . . . O X X X . O . |
$$ ---------------------------------------[/go]


This White 158 starts the Capture version.

Click Here To Show Diagram Code
[go]$$Bm159 159
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O . . . O . O X X X O . O O |
$$ | O O O O X X O O . . O O O O X . . X . |
$$ | O X X X . X . O O . O . O O X X X X X |
$$ | O X X X . X . O . . O O X X X X O O O |
$$ | O O O X . X O O . O O X X O O O O X . |
$$ | . O O O X . . O . O O X . O O . X X X |
$$ | X . O O X . . O . O . X O O X X X O O |
$$ | . O O X X . . O . O . X O . O . X X O |
$$ | O O O X O X . O . O O X X O O O X O O |
$$ | O O X . . X . O . O . O O X X X O O O |
$$ | O X X , X X . O . O O O O X O X O O X |
$$ | O X . . O X O O . . . . 1 O O X X O X |
$$ | O X X . X O . O O O O O O X O X . O X |
$$ | X X . . X O O O . . . . O X X X . O . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Wm160 160-164
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O . . . O . O X X X O . O O |
$$ | O O O O X X O O . . O O O O X . . X . |
$$ | O X X X . X . O O . O . O O X X X X X |
$$ | O X X X . X . O . . O O X X X X O O O |
$$ | O O O X . X O O . O O X X O O O O X . |
$$ | . O O O X . . O . O O X . O O . X X X |
$$ | X . O O X . . O . O . X O O X X X O O |
$$ | . O O X X . . O . O . X O . O . X X O |
$$ | O O O X O X . O . O O X X O O O X O O |
$$ | O O X . . X . O . O . O O X X X O O O |
$$ | O X X , X X . O . O O O O X . X O O X |
$$ | O X . . O X O O . . . . X 3 1 X X O X |
$$ | O X X . X O . O O O O O O X . X 2 O X |
$$ | X X . . X O O O . . . . O X X X 4 O 5 |
$$ ---------------------------------------[/go]


White 160 is the Oki of Joachim Meinhardt, being the death blow to the "classical" solution.

Click Here To Show Diagram Code
[go]$$Bm165 165-174
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O . . . O . O X X X O 4 O O |
$$ | O O O O X X O O . . O O O O X 0 6 X . |
$$ | O X X X . X . O O . O . O O X X X X X |
$$ | O X X X . X . O . . O O X X X X O O O |
$$ | O O O X . X O O . O O X X O O O O X . |
$$ | . O O O X . . O . O O X . O O 9 X X X |
$$ | X . O O X . . O . O . X O O X X X O O |
$$ | . O O X X . . O . O . X O 8 O 7 X X O |
$$ | O O O X O X . O . O O X X O O O X O O |
$$ | O O X . . X . O . O . O O X X X O O O |
$$ | O X X , X X . O . O O O O X . X O O 3 |
$$ | O X . . O X O O . . . 2 X O O X X O 1 |
$$ | O X X . X O . O O O O O O X . X X O 5 |
$$ | X X . . X O O O . . . . O X X X X O O |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$Bm175 175-177
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X X O . O X . |
$$ | . . . . X O O . O O O X O X O . . O . |
$$ | . . . X . X X O . . O X O O . O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O . . . O . O X X X O O O O |
$$ | O O O O X X O O . . O O O O X O O X 2 |
$$ | O X X X . X . O O . O . O O X X X X X |
$$ | O X X X . X . O . . O O X X X X O O O |
$$ | O O O X . X O O . O O X X O O O O X 1 |
$$ | . O O O X . . O . O O X 3 O O X X X X |
$$ | X . O O X . . O . O . X O O X X X . . |
$$ | . O O X X . . O . O . X O O O X X X . |
$$ | O O O X O X . O . O O X X O O O X . . |
$$ | O O X . . X . O . O . O O X X X . . . |
$$ | O X X , X X . O . O O O O X . X . . X |
$$ | O X . . O X O O . . . O . O O X X . X |
$$ | O X X . X O . O O O O O O X . X X . X |
$$ | X X . . X O O O . . . . O X X X X . . |
$$ ---------------------------------------[/go]



Click Here To Show Diagram Code
[go]$$ The End
$$ ---------------------------------------
$$ | . . . . . X . O . . O X X B W . O X . |
$$ | . . . . X O O . O O O X O X W . . O . |
$$ | . . . X . X X O . . O X O O C O O . . |
$$ | . X O , X . X O . O O X . O O X O . . |
$$ | . . X X X X O O O . O X X O X X O O . |
$$ | X X X O O O . . . O . O X X X O W W W |
$$ | O O O O X X O O . . O O O O X O O X O |
$$ | O X X X . X . O O . O . O O X X X X X |
$$ | O X X X . X . O . . O O X X X X . . . |
$$ | O O O X . X O O . O O X X . . . . X X |
$$ | . O O O X . . O . O O X X . . X X X X |
$$ | X . O O X . . O . O . X . . X X X . . |
$$ | . O O X X . . O . O . X . . . X X X . |
$$ | O O O X O X . O . O O X X . . . X . . |
$$ | O O X . . X . O . O . O O X X X . . . |
$$ | O X X , X X . O . O O O O X T X . . X |
$$ | O X . . O X O O . . . O T O Q X X . X |
$$ | O X X . X O . O O O O O O X T X X . X |
$$ | X X . . X O O O . . . . O X X X X . . |
$$ ---------------------------------------[/go]


Black has 62 points of territory + 39 prisoners = 101 points in total.
White has 48 points of territory + 48 prisoners = 96 points in total.

Black wins by 5 points here.

Please be aware that the Guzumi destroyed 3 points of White's territory in the top right and the Hasami-Tsuke 4 points (circled), compared to the "classical" solution. Without these two moves (= the "classical" solution), White would win by 2 points, due to Joachim's Oki, which destroyed 4 points of Black's territory in the lower right (triangled).
Last edited by Cassandra on Mon Feb 28, 2011 11:40 am, edited 2 times in total.
The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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Cassandra
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Re: The really most difficult problem ever

Post by Cassandra »

The sequences of the posting above in one SGF.

The really most difficult Go problem ever: https://igohatsuyoron120.de/index.htm
Igo Hatsuyōron #120 (really solved by KataGo)
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