Probably the most important part of our publication contains a story about attitude, power of endurance, collaboration, serendipity and time ...
tl;drThe story begins in 1999, when Joachim Meinhardt 4k from Frankfurt / Main got interested in studying Igo Hatsuyôron 120 for himself, based on a solution sequence that he found at goproblems.com (introduced as "Dosetsu's problem" by Merlijn Kuin 6d from Amsterdam).
Simple arithmetic resulted in the first inconsistency found:
The problem looks like a middle game position that – in principle – could have been taken from a real game. However, there are 71 white stones on the board, but only 70 black ones. So what happened to Black's 71st stone?
There is (only) one place at the lower right edge of the board, where White could have captured a black stone, and connected afterwards. This implies that the solution sequence must provide Black with a lead by at least two points on the board to enable him winning the game.
Unfortunately, the solution at goproblems.com did not include any moves of the succeeding endgame sequence on the left side of the board, after the complete dissolving of the hanezeki in the lower right in the Capture Variation. The final result was specified as "Black + 2".
Therefore, Joachim had to try on his own. His best guess for the endgame resulted in "Black + 3" on the board. This was a strong indication that his assumption of the missing black stone might have been correct, resulting in the given final score of "Black + 2".
Nothing serious had happened yet, and Joachim's investigations came to a pause in 2002.
However, in 2005, Fortuna decided to let the wheel of fortune make a lucky turn.
The German Go Journal published an article about the solution to "The most difficult problem ever". But no, this article was not about Igo Hatsuyôron 120, but about Xuanxuan Qijing's famous problem 大鐵網勢 ("The Big Wire Net", also called "The Emperor of Tsume-Go").
Coincidentally, Joachim was directed to the internet pages of Jérôme Hubert 3d from Paris, where he stumbled over another, alternative, solution sequence to Igo Hatsuyôron 120 (probably taken from the 1988 book on "Weiqi Fayanglun" – Chinese for "Igo Hatsuyôron" – by Cheng Xiaoliu 6p, of which we had no knowledge before 2009). He suddenly realized that – in his self developed sequence for the mutual occupation of opponent's liberties in the Main Semeai – White had only occupied "absolute" neutral points, leaving some valuable points untouched. With Hubert's modification, White was able to capture Black's single stone in the lower right quadrant of the board (but there was a compensation of one point for Black in return, due to the now changed sequence), gaining an overall advantage of one point, compared to Joachim's old sequence.
The final score was reduced to "Black + 2" on the board, so considering Black's missing 71st stone resulted in an "ideal" result of "Black + 1".
Nothing serious had happened yet, but the wheel of fortune was given another lucky turn.
Thereafter, Joachim got to know the 1982 Go World article by Fujisawa Hideyuki 9p (in principle having the same contents as the Japanese original), titled "The most difficult problem ever".
In one of the subvariations to his solution, Fujisawa Hideyuki displayed a semeai between White's group at the bottom, and Black's large group in the upper right (the "usual" Main Semeai applies to White's group at the left edge of the board), which Black wins by one move. During the sequence of dissolving the hanezeki (after White captured the hanezeki's tail, and Black recaptured four white stones), White used a placement in the now empty area for attacking Black's group in the corner.
This resulted in the second inconsistency found by Joachim: Fujisawa did not use this placement in his solution sequence (wherein the hanezeki's tail is captured much later in the game). Joachim tried this himself and found that White could gain a total advantage of two points by using this "late" placement.
Now, White achieves a jigo (draw) on the board, so the question of Black's missing 71st stone was reopened again, in the light that it can be considered absolutely unlikely that Inoue Dôsetsu Inseki created a problem to fulfil the task "Black to play and lose by the smallest margin possible".
At least, "Jigo" (without the consideration of a missing black stone) might have been a reasonable result for finishing a given middle game problem, would there not be the remaining contradiction to the given task for solving Igo Hatsuyôron 120, "Black to play and win".
Joachim's new findings were also published in the German Go Journal, but still nothing serious had happened yet. Who in East Asia would be really interested in reading a Western Go Journal, aimed at an amateur audience?
However, this was the moment, when I got interested into the problem. I tried hard to find a spot on the board for placing Black's still missing 71st stone, but was unable to find any that did not massively hurt one of the known variations. It was also impossible to take any of White's existing stones off the board, for the same reason.
But Fortuna intended to make fun of Black once again.
In 2007, Benjamin Teuber 6d from Hamburg got the opportunity – during a study visit in Korea – to present Joachim's findings to Yamada Shinji 6p from Japan. Yamada Shinji enhanced the solution sequence for White by introducing another option for reducing Black's upper left corner. The "Tsuke of Yamada Shinji" was born, providing White with a further gain of two points of territory. Black is unable to resist, otherwise he would suffer from an unbelievable seki in that corner.
Now, White achieves a win by two points (on the board), totally upsetting the known professional solutions.
As long-time editor of the "Problem Corner" of the German Go Journal, I was very well aware of a special characteristic of tsume-go problems: There must be a solution. If you do not see any, try harder, and do so again and again.
From now on, the wheel of fortune turned the other way round, favouring Black.
My first finding was only a tiny, and still insufficient, one.
In his Go World commentary, Fujisawa Hideyuki said that Black must not throw-in for a second time in the upper part of the hanezeki. The reason given was that Black's upper right group lost a decisive liberty by this exchange, and that this led to an unfavourable outcome in a semeai. Despite searching hard, I was unable to find such a semeai, and since then compensation for Black's missing 71st stone seemed to be available, as Black's additional early sacrifice counter-intuitively resulted in a net gain of one point for him in the Capture Variation.
But Black furthermore lacked an additional three points for winning the game.
The discovery of Black's game-decisive move in the upper right corner, a guzumi ("usually" considered to be a "bad shape" issue), took me about three month of continuous intense analysis, including the detection of a suitable moment for playing this move successfully (i.e. just before the hanezeki's tail has reached its maximum length).
This guzumi destroyed three points of white territory in the Capture Variation, so wining the game for Black again. It results the "ideal" final score of "Black + 1" (now including Black's missing 71st stone, due to the earlier found second throw-in in the hanezeki).
Everything was OK now? No way!
Unfortunately, the guzumi is gote locally. White has a wild bunch of options for playing tenuki that include very difficult considerations in the upper left corner, as well as long endgame sequences. Many of the most promising tenuki options ended in a range from "Black + 1" to "White + 1", relying on deficient amateurish endgame capabilities.
In 2008, at the European Go Congress in Leksand, Sweden, I tried to get some Chinese professionals interested in our solution, but in vain. At least, Cheng Xiaoliu seemed to have got some stimulation for his forthcoming 2010 book on Weiqi Fayanglun.
After I had invested two years of intense study into the consequences of the guzumi, Fortuna showed mercy, and turned the wheel of fortune again.
In 2009, Harry Fearnley 2d from Oxford joined our team, being excited about "beast" on the Go board, especially about all sorts of strange seki.
Harry introduced "his" hasami-tsuke in the upper right corner, and asked a simple question: "Did you ever consider this common endgame technique for reducing White's territory?"
In conjunction with the guzumi, Harry's hasami-tsuke destroyed another four points of White's corner territory, bringing all the close results after White's tenuki options on the safe side, hopefully compensating for all the weaknesses in amateurish endgame sequences.
If White answers Black's guzumi locally, a final score of "Black + 5" results in the Capture Variation, so White will choose the Semeai Variation, instead, that gives her the better result of "Black + 3". As it eventually turned out, none of White's tenuki options provided her with a better score than this.
From now on, our further investigations revealed only technical issues (e.g. changes in the order of moves), but did not affect the final score any longer.
Harry found a "Circular Hanezeki" (arising only after mistakes from both sides), a theoretically predicted "beast", but that has not yet been underlined with a concrete example.
We detected that it would be technically best to play Harry's hasami-tsuke first and the guzumi thereafter.
Joachim focused on potential alternatives to the guzumi.
Trying to defend the upper left corner (after the Crosscut Sequence in the centre), instead, resulted in a semeai between White's group at the top and Black's large group in the upper right, which includes a very complicated ko fight (i.e. "Joachim's Ko-Semeai"). We analysed a wild bunch of variations, but eventually we had to conclude that Black will be unable to win this line of play.
Capturing White's group at the left does not work either.
Our intense work on "Joachim's Ko-Semeai" –and thus also on the problem itself – stopped in 2014.
Recently, our hiatus was interrupted temporarily.
Harry found a flaw in the order of moves in our solution, concerning the timing of the atari in the hanezeki.
Joachim analysed the effects of using Michael Redmond's kikashi in the professional solution.
Studying Igo Hatsuyôron 120 is of no practical use for today's professionals. The problem is extreme complicated and very challenging, so even a professional needs a lot of time for diving deep enough into this problem. Utilizing other (modern) sources is much more efficient in order to become stronger.
Therefore, we are very grateful that some (also semi-) professional Go players – with connections of various intensity to the Western Go world – kindly spend a tiny amount of their valuable time to glance trough our materials, and assisted us with valuable hints. I strongly suppose that these professionals "felt" something in our amateurish work that reminded them of something similar to professional attitude.
Following the rough estimation of Kang KyoungNang 7d from Korea, it seems very unlikely that Black could successfully dispense with creating the hanezeki in the very beginning of the solution sequence.
She also put us in contact with Professor Jeong SooHyun 9p from Myongji University in Seoul.
Prof. Jeong was kind enough to tell us that there didn't seem to be any major problems within our sequence (I think that this was no confirmation that our solution is correct).
However, he also pointed out that two points should be corrected. The Hanezeki Exchange should be played later, and the endgame on the left side of the board should be started much earlier than we did so far.
Ôhashi Hirofumi 6p corrected the move order for filling the five-point nakade.
Michael Redmond 9p showed us some astonishing tesuji in the tenuki variations after the guzumi. He also introduced "his" kikashi in the bamboo joint as a usual technique for providing Black's large group in the upper right with an additional liberty. However, in the problem, Black has no use for this gain.
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