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© 2013, Thomas Redecker, Berlin.

The most difficult problem ever: Igo Hatsuyôron 120

Thomas Redecker

with the participation of

Joachim Meinhardt & Harry Fearnley

Buy the full book at gobooks.com

Great works are performed, not by strength, but by perseverance

Samuel Johnson, 1709 – 1784

The most difficult of all Go problems, created by Inoue Dosetsu Inseki (1646 – 1719), has still not been solved by professional Go players. The long-standing collaboration of three amateurs from Germany, and the United Kingdom, has now found the answer!

This book celebrates the problem-collection’s 300th anniversary and is the most comprehensive collection of information that is known about this stunning problem. Half of the book is filled with what the authors believe to be the solution to the problem, including an in-depth treatment of the failed lines. The race towards the right solution was started by professionals who laid substantial and significant foundations, but seemingly amateurs finished it.

All move sequences (of the main lines, as well as of the sub-variations) are explained in great detail. The same is true for the additional work on theoretical issues that are fundamental to the problem (e.g. hanezeki, approach-move liberties, and ko).

You might recognize this book as
– Attempt to provide a solution to Dosetsu’s masterpiece,
– Complete analysis of a middle-game position,
– Evidence that time might be able to compensate for a large gap in playing strength,
– Search for the truth, or
– Attempt to show the beauty, and depth, of the game of Go.

Possibly, after having studied this book, you might be able to grasp a feeling that only those players can be named real masters of the game, who have left their boundaries behind them.

Copyright Page

According to Japanese customs and the usual order in East Asia with names of persons, we will always list the family name before the given name.

3rd edition.

© 2013, Thomas Redecker, Berlin.

Alle Rechte, auch die des auszugsweisen Nachdrucks, der fotomechanischen Wiedergabe und der Übersetzung, vorbehalten. Dies betrifft auch die Vervielfältigung und Übertragung einzelner Textabschnitte durch alle Verfahren wie Speicherung und Übertragung auf Papier, Transparente, Filme, Bänder, elektronische und andere Medien, soweit es nicht §§ 53 und 54 URG ausdrücklich gestatten.

The board graphic for the book cover was created using Multigo©: http://ruijang.com/multigo/

Table of Contents

The Problem

The Solution

Foreword to the Anniversary Edition

Legend

Content of the Revisions

PART 1: OUR SOLUTION

A Summary of Our Solution

Stage 1 – Preparatory Works

Technical Notes (I)

The Main Path of Our Solution (I)

Variations of Our Solution (I)

Stage 2 – The Problem’s Real Problem

Technical Notes (II)

The Main Path of Our Solution (II)

Variations of Our Solution (II)

Stage 3 – The Dust Settles

Technical Notes (III)

The Main Path of Our Solution (III)

Variations of Our Solution (III)

Variations’ Map

PART 2: PROFESSIONAL’S SOLUTION

The Professional Solution

The Main Path of the Professional Solution

Variations of the Professional Solution

The Evolution of Professionals' Knowledge

PART 3: AMATEUR’S KNOWLEDGE

The Evolution of Amateurs' Knowledge

The History of the Problem’s Final Score

The Further Evolution of Amateurs' Knowledge

The Decisive Moment in the Historical Line of Play

Hidden Aspects of the Oki

Guzumi at Top Right

Various Kikashi in the Hanezeki

PART 4: FURTHER TOPICS

Further Structural Elements of the Problem

About Approach-Move Liberties

About Hanezeki

About Ko in a Semeai Between Two One-Eyed Groups

Igo Hatsuyôron 120 and Go Playing Programs

Acknowledgements

References

Short Biographies

Glossary

Buy This Book

About SmartGo Books

Dieses Buch Kaufen

Über SmartGo Books

The Problem

igo.hatsuyoron.120 <1/0>

Black to play (and win)

The Solution

our.solution <3/0>
22 at 19; 94: connects

our.solution.sub101 <14/1>

our.solution.sub117 <20/1>

our.solution.sub153 <24/1>

our.solution.sub161 <24/4>

our.solution.sub164 <27/4>

our.solution.sub169 <30/4>

our.solution.sub177 <63/18>

Black wins by three points

Foreword to the Anniversary Edition: Igo Hatsuyôron 120 – Re-Evaluation by Amateurs

The Igo Hatsuyôron is a classical Japanese collection of Go problems, written 300 years ago, in 1713. In 1982, Fujisawa Hideyuki 9p published the “lost” problem 120 (found by Araki Naomi in an old edition), and produced a solution with his study group. The main results were also given in an English-language article in Go World, Autumn 1982-issue, edition 29.

By the beginning of the 21st century, several other proposed solutions could be found, in both Chinese (Weiqi Fayanglun), and Korean (Wiki Balyangron), not only in books, but also on the Internet. The sequences reported as “correct” differed from each other in some details.

They all shared one thing: At a very critical moment they did not take into account the strongest resistance by White. This fact was uncovered by Joachim Meinhardt, a German Kyu player, after several years of work, and published by me in 2005 in the Deutsche Go-Zeitung (= German Go-Journal) under the headline “The really most difficult Go problem ever”. It said that the goal of “Black to play, and win” had not been reached.

In 2007, at the suggestion of Benjamin Teuber 6d, Yamada Shinji 6p was kind enough to spend some of his valuable time on Joachim’s finding. Yamada Shinji found a further improvement for White, making more problems for Black.

At the end of 2007, I discovered a move for Black, which was not mentioned in the literature to date. This move – a guzumi – gains three points for Black. Perhaps it can re-open the path to a win for Black?

In the following years I worked intensively on the variations following my guzumi. Yoon YoungSun 8p was kind enough to give me the endgame sequences for some essential ones.

In 2009, Harry Fearnley from the United Kingdom brought a follow-up move into play that, combined with the guzumi, gives Black a further gain of four points (in one of two significant main variations).

In June 2011, we published the first edition of this book as a summary of our work, and of what we knew to have been published up to mid 2010. Our thanks go to Gunnar Dickfeld from Brett-und-Stein (= “board-and-stone”) publishing house, who made this first publication possible.

This problem is not a simple life-and-death problem. It is a complicated whole-board problem. We think that it is the most interesting, and difficult, problem in any of the classical problem books. For that we have to thank Inoue Dosetsu Inseki.

It is really unusual (perhaps unique) to have a whole book about a single problem. Our reason for writing the book was that we wanted to obtain a definitive solution to the problem. We know that we have found aspects, which were missed in previously published solutions, and thought that we had to publish our proposed solution, so that others could look for errors in ours, and so arrive at the correct solution.

Furthermore, the problem itself is very unusual, and we thought that some others might also enjoy getting a fuller understanding of its complexity.

Because the problem is a whole-board problem, we have to be concerned about the territorial result – this is normal. Yes, this makes it more like analysing a “normal” game. As is usual in traditional problem books, the problem says simply “Black to play”. This assumes the addition of “… and get the best result” – in this case this must mean “… get the best final score – at least win, rather than lose”. There are two possible large Black sacrifices. White will choose which group to capture. Black’s problem is to make sure that whichever one White captures, White will still lose!

In 2010 Cheng Xiaoliu 6p published his second book on Igo Hatsuyôron. We could not consider this book in our first edition. Many of his results confirmed our earlier ideas. Nevertheless, our assessment of the correct solution is not affected by Cheng’s newer findings. We have used this special edition to integrate results of his newer analysis. In addition, we have included discussions of further variations from other sources known to us.

We have now completed our investigations into the correct order of moves in the top right corner, after the guzumi.

We also added some new results on the first moves of the solution, and on some obscure aspects, which arise during the building of the hanezeki in the lower right corner.

Our latest investigations relate to two very irritating semeai, found by Joachim, which could arise in the professional line of play. We edited the corresponding chapter after the first printing of the special edition in March 2012. We never imagined that – from the known comments – something that looked so simple could become very confusing, and complicated.

Our special thanks go to Kang KyoungNang 7d, and Professor Jeong SooHyun 9p as well as his students at Myongji University in Seoul, who – despite being extremely busy with their usual tasks at the University – were so very kind to work long and intensively with our solution and give us valuable information, especially concerning our new results. Kang KyoungNang helped us with variations for the very first moves and established the contact with the Myongji University. The contributions of Professor Jeong and his students brought us past the guzumi, and allowed us to focus on the correct line of play for the endgame on the left side.

In May 2012, I was very pleased to get the opportunity to meet Kobayashi Chizu 5p, and Ôhashi Hirofumi 6p, at the Nihon Kiin during a stay in Japan. Ôhashi Hirofumi did not seem to be uninterested in our work (collected in a second, largely extended, but unpublished, edition) and also had prepared some suggestions about the correct order of moves for filling the nakade on the left side.

We are very delighted that Michael Redmond 9p has shown great interest in our work. He got in touch with the problem during a teaching visit of the United Kingdom in Spring 2013. We owe Michael many valuable comments and very interesting insights into the professional mindset.

Michael validated the strongest tenuki variation after Black’s guzumi, including improvements for many of our sub-variations. He also drew our attention to a kikashi in the bamboo joint in the upper right corner, which was not previously noticed by us.

As the second edition of our work this third edition exists in a bound form in only a few copies, most of which are reserved to the authors.

We are therefore delighted that Anders Kierulf has added our book to the library of his SmartGo Books. So, much more interested Go players than ever should be able to find access to its very specific content.

Please understand that not all aspects could be optimized for viewing on the screen. The conversion into the required format had to be done “on the fly”, because the updating of the written contents kept running in parallel.

To further enable the reader to facilitate access to the certainly very complex matter, we have decided to extend the explanations of the structure of the problem and its internal dependencies significantly, and also to expand the theoretical explanations in the back of the book.

This reconstruction of the book led to a division of the solution into three distinctive sections, and to the introduction of “Technical Notes” to enable an in-depth study for those who are particularly interested into the problem.

After a placative “Summary of Our Solution” as an entry we start our book by presenting our solution (ending with a three-point victory for Black) and its variations.

We continue by presenting the latest professional solution (by Cheng Xiaoliu), and its specific variations. This is a sequence of professionally published best moves for both sides, but ending with a jigo only.

This is followed by a historical review, both of the development of knowledge published by professionals as well as of our own findings.

Subsequently, we describe the impact of the move found by Joachim, which puts all the professional solutions in question. We then proceed to the analysis of my bad shape move.

The latter part of the book describes special structural elements of the problem. Some readers may want to read some chapters – e.g. on approach-move liberties, or on hanezeki – out of sequence, as they first encounter these topics in the book.

Please understand that, in the light of the degree of difficulty and complexity of the problem, we have shown some longer move sequences repeatedly at various points throughout the book. Also – with the exception of most ko sequences – we have tried to show all moves in diagrams, so avoiding the use of “x at y” when a stone is played on the point where another one was captured.

We hope this book helps to find a reliable solution to this most difficult of all Go problems. We would be delighted to receive any comments, criticisms, or suggestions. Please do this via our e-mail account TRMDPE@t-online.de.

In 2012, I visited the classical Japanese landscape garden at Katsura Imperial Villa in Kyoto, where even one lifespan does not seem to be sufficient to explore all of its beauty. Igo Hatsuyôron 120 seems to me to resemble such a typical Japanese garden. Nothing can be added, nothing can be changed, and nothing can be taken away, without destroying the harmony of the garden (i.e. the solution here).

No one but a genius will be able to construct such a garden and to find the primary path for walking through it. However, after enjoying the garden for several years, we simply asked “Has this special viewing line ever been recognized before?” And, surprisingly enough, apparently nobody had seen it before.

Igo Hatsuyôron’s problems were designed to push forward the frontiers of Go technique by presenting the most difficult problems which people could actually solve. In problem 120, the exact position of each stone on the board matters, and the various parts and aspects are so well integrated with each other that it is hard to believe in coincidence, so making the problem an artistic masterpiece. We play Go because we admire such great depth and skill, as shown by Inoue Dosetsu Inseki.

We would like the reader to view this book – celebrating the 300th anniversary of Igo Hatsuyôron – as an encouragement to push one’s analytic efforts to the limits of one’s abilities. If you not only enjoy the experience, but find that it is enlightening, and leads to an improvement in your Go playing, we will be very pleased.

Berlin, July 2013

Thomas Redecker

Legend

@@@ Further details can be found at “please click here”.

<22/33> At the end of the sequence shown, there are 22 black, and 33 white, captured stones.

<22*/33> As above, but the missing 71st black stone is not counted as white prisoner.

55 / 66 Black’s move number 55 / White’s move number 66.

99: ( –VAR-> @@@ ) A variation for move Black 99 can be found on page “please click here”.

88: (B –VAR-> @@@ ) Variation B for move White 88 can be found on page “please click here”.

VAR{P} 99 Variation for move Black 99 {of the professional solution}.

VAR 88 {(A)} Variation {A} for move White 88.

VAR 77 {(.2)} 88 Variation for move White 88 within the variation {.2} for move Black 77.

55: (* @@@ <- – *) Move Black 55 is a variation of a move that can be found in a diagram on page “please click here”.

& {$} / % {#} Black / white point of territory. { additionally, a white / black prisoner is counted }

[Lit. 5{; p. 222}] The text above is based on “Literature” [Lit. 5 { ; page 222 }].

/// 33 Break in the sequence shown; move Black 33 does not immediately follow the previous diagram.

Please take notice!
The work on the printed version of this book is still in progress.
Large parts of the English text must still be transcribed into native English.

Our Solution

A Summary of Our Solution

We wrote this synopsis primarily to give an outline of Our Solution, but also to highlight some of the problem’s main features and interdependencies, in an attempt to clarify the structure. Although the style may be unfamiliar, we hope that it will be helpful, for reference purposes. You will find a further overview that highlights technical details in more depth in the chapters “Technical Notes”. For a more historical outline, please see here.

The Birth of the Hanezeki (Dia 1)

story.000 <-Dia 1->

In Dia 1, at the very beginning, ///&/=/&/= are all weak. The other groups can live. can get two eyes, but then must let /& live at lower right, and & will probably die. If all major groups live, is most likely to win with more territory.

1 primarily threatens the life of /&, and only secondarily threatens to connect , and &. tries to connect , and . If succeeds, then dies. If dies, and does not kill a big group, then loses.

If we look ahead (Dia 6): there will be a liberty race between /, with //&/=/= and # temporarily caught in between! $ is stable, and not involved in the fighting below.

Some Unexpected Sacrifice (Dia 2)

story.015 <-Dia 2->

Neither player succeeds, and gets cut off, as do / (forming a simple seki).

now plays some kikashi, spoiling ’s shape, which will make life easier for him in a far future.

still does not try to build two eyes for , with 17 at 18, instead. The territorial balance is still in ’s favour overall.

19 (which we call the “second throw-in”) is a surprising sacrifice that was assumed for decades to be harmful for the solution or at least would lose points unnecessarily.

The Birth of the Hanezeki’s Tail (Dia 3)

story.027 <-Dia 3->

Neither &, &, nor , can live independently; cannot link out to the left. By Dia 3, &/=/&/= form what is almost a hanezeki (a strange seki, where both players can capture, but normally neither wants to)! Only the tail is still missing – it starts with 27. The dotted path through ’s potential territory in the centre will become a one-way street.

Both =, and =, will be either captured together (the regular case), or they will live together (the exceptional case). Due to their closely tied co-existence, we will further neither mark, nor mention, them.

The groups in the hanezeki will remain untouched for a long period of time; we will not mark them temporarily from here on, until they get into focus again.

Calm Before the Storm (Dia 4)

story.069 <-Dia 4->

The hanezeki’s tail, #, wanted to escape, but could not, and kept growing bigger.

wanted to stop the growth of the hanezeki’s tail, #, which destroys her potential territory in the centre, but could not. Else would lose her stones in the lower right corner, and so the game.

On the other hand, the larger # becomes, the better for , should she ever get the chance to capture #.

At the end of Dia 4, #, and $ cannot connect.

Before carrying on with the main business, takes the chance to play some forcing moves (F/H/J), at no cost to himself, but reducing ’s potential territory in the top right corner, for the time being.

Now, after her large territorial loss in the centre, cannot allow to simply get two eyes in the upper right corner any longer. In the meantime, the territorial balance has shifted in ’s favour.

Michael Redmond 9p kindly drew our attention to the kikashi L in the bamboo joint, which “naturally” gains an additional liberty for . However, has to recognize that only one additional liberty does not really help with the semeai, so he waived this move.

The Problem’s Real Problem (Dia 5)

We now have reached the very critical moment of the problem, which confronts us with the real challenge that is hidden in Igo Hatsuyôron 120: to play and win.

story.071 <-Dia 5->

has three main options now.

(I) He can immediately bump the tail’s head against ’s stones on the left side, with a move at A – following the classical line of play – …

(Ia) … to attack the -group on the left side, or …

(Ib) … to attack the -group on the upper side, …

… aiming at forcing to capture #, so saving .

However, by following option (Ia) – the classical line of play again – will be taken by surprise over 60 moves later, and lose the game by a small margin.

Black also cannot hope on a semeai against ’s group on top – option (Ib) leads to a very complicated ko-fight that ends with a win.

(II) After a long search, found the very calm, and contained, move of 71 (the Guzumi), which further destroys ’s potential territory in the corner and re-opens the path to success.

After 71, has to make a big decision. has the option to play tenuki at top right, and let live, while hoping that she can get sufficient compensation by attacking $/!, and parts of %, on the left side. However, after much analysis, sees that this option does not provide a better result for her than 72, and so she has to play 72, which stops from getting two eyes.

It is 71, and the previously played forcing moves H/J, which are the main reason that our solution looks different from the Solution of Fujisawa Hideyuki 9p. Please refer to the end of this tour to see why Fujisawa’s Solution does not work any more.

This edition includes both the English and German text.