Appendix A: some (badly connected) thoughts upon the "theory" of go problems.

Appendix B: a few tries at (almost) rigourous definitions.

Introduction and user's guide

Why a bestiary ?



In the many years I have devoted to the game, I have collected strange situations, famous tesujis and other wonders. Some could be found in my Des manœuvres étranges (published in the French Go Review), and others were published in earlier articles, or appeared on my problem pages, but only a few of my favorites figured there. In 2005, I decided to gather them all here, but this was for a long time a work in progress (and is still somewhat unfinished : see the list of recent additions above ; here is the complete story). In August 2006, this bestiary was added (with slight improvements) to Games of Go on Disk (GoGoD), T. Mark Hall and John Fairbairn's project ; I owe them many new references and corrections to the anecdotes told here... During the summer of 2009, I included sgf files allowing for a much better analysis of some positions, as will be detailed below. But all this work (which is far from complete : in 2010, only the files for the first part were written) is still pehaps marred by mistakes and lack of precision ; don't hesitate sending me criticisms and comments (at ).



One of my aims in those pages was to explain, to the best of my capacities, why those situations are noteworthy, those explanations being aimed at a level of (about) 5 kyu. Alas, solving some of those problems (or even understanding fully the solution) asks for a much higher level : Dosetsu's problem, usually described as the most difficult ever, required literally hundreds of hours to be solved by professionals ; in such cases, you cannot expect from an amateur any kind of exhaustive commentary, and even less an easily understood one ... To compensate for this, I have also illustrated those positions with more or less technical remarks and anecdotes ; some are generally unknown in the West (which doesn't mean I have forged them ), like the story of the shrine problem ; I hope, by so doing, that this oral tradition (a large part of which has been told to us by Master Lim Yoo Jong) will not be lost...



One will find here wonderful positions and exquisite moves (such as Dosaku's warikomi or the external atekomi of problem II.4.4), but also situations which would rather be ignored by most players, like the (in)famous molasses ko ; those monsters are the reason Harry Fearnley called his own collection, from which I borrowed a few specimens, a bestiary ; I must add that those problems have no real copyright (and anyway, I have some strong feelings (in French) with respect to abuses of the intellectual property concept), but I have tried, as far as possible, to give precise references ; here again, I will be grateful for any further information... Many of them appeared first in two famous classical collections, Xuan Xuan Qi Jing (Chinese, 14th century) and Igo Hatsuyoron (Japanese, early 18th century), which I will describe in more detail later, and which were already bestiaries ; I also found some of them in a set of (somewhat) easier and more practical problems, collected by Hayashi Gembi, the Gokyo Shumyo. I have not always respected the original settings of these problems, either voluntarily (for instance to show the theme without unnecessary complications) or more often because I did not have access to them ; I could now rectify this, but as, anyway, those settings often differ from one edition to the other, I feel somewhat forgiven for whatever liberties I have taken (in every sense of the word)...



Finding one's way in this maze



The classification of problems made here (and summarized in the table of contents above) is not intended to be rigid and definitive : some themes often appear as variations in problems mostly belonging to some other category ; some life-and-death problems are in fact live-or-escape ones, etc. I therefore often give cross-references : for instance, Dosetsu's problem (the most difficult ever) refers to the position known as hanezeki. As a private homage to Nicolas Bourbaki, those references are "relative" ones, i.e. Dosetsu's problem is problem 4 in its subsection, but would be mentioned (if it had no name) as problem 7.4 in the first part of the bestiary, and as problem I.7.4 everywhere else...



While most of those problems are "artistic" ones, they are still also often quite hard ; therefore, I thought it could be useful to give a (very rough) indication of their difficulty (each section ending usually with the most difficult ones); a few easy reference diagrams are not ranked, but for the others :

one means that a player around 1k should be able to solve the problem (within a few minutes at most and without putting stones on the board); there are 53 problems in this category,

two mean (with the same conditions) a 5d level; there are 61 problems of this type,

three mean a professional level, with no real time limits, as they are able to think efficiently for a long time... (41 problems).

And, of course, Dosetsu's problem, and 12 others, not so hard, but still inaccessible to mere mortals (at least without trying variations on the board), are ranked four ...



To be complete, I must add that this classification presupposes you do not have any hint other than the problem's caption (it is distinctly easier to solve a problem knowing that it uses under-the-stones play, say), and, of course, have never heard about it in advance, as could well be the case for the most famous ones, which many strong amateurs may at least already have glimpsed in some book or magazine ; this explains why some problems (especially those of section I.5) are hard to rank ; in those cases, I have used marks like (?), for instance. With these provisos, for a kyu player, solving a problem is a performance which he could legitimately be proud of...



User's guide



Problem solving is usually supposed to improve the practical level of players ; many collections of problems are introduced by hints for good use. Two quite distinct approaches are to be found (which does not mean they are mutually exclusive) : Chinese players suggest that you should look at a large number of positions as fast as possible, look then at the solutions, try to find them again some time later, and so on, until the eye and the brain get accustomed to see immediately the correct move or sequence ; some Japanes pros, on the other hand, will tell you to stay on a problem until you have solved it completely (which means you have considered every possible resistance, and perhaps even refutated every wrong solution). But anyway, everybody agrees to say one must not put sequences on the board (except those of the initial setting). Actually, for training purposes, one should not even need the captions : in a real game, nobody stands at your shoulder to tell you that this group can be killed, or that this other one can connect to the outside... So, if you would rather see those lists as sets of problems to be solved, you will find them there, with only the captions (like "Black to play, status ?" or "White to play and escape") ; but of course, some of the problems I show here are so hard that it would be somewhat absurd to try to solve them by following those recommandations to the letter, except for professional players ; to appreciate these masterpieces, it is probably better to try some variations before looking at the solution (which will often be not too easy to understand even after those tries).



Alas, the solutions given here as static diagrams allowed me only to give but a few variations, not to mention the fact that for under-the-stones solutions (and for some other very long ones), they were almost useless ; I had tried to improve this by using the Java applet of Hiroki Mori, to give animated variations (clicking on the corresponding link will open a new window using it), and some of those problems be found on other sites, like the GoProblems site ; when appropriate, I also gave a link towards their solutions. But during the summer of 2009, I began to included sgf files which you can open by clicking on the highlighted part of the caption (at least if your browser is correctly parametered ; the happy users of GoGoD will probably choose to read those files with Pbase, for the others, Cgoban should probably be give good enough results) ; those files include the solution, main variations, refutations, and some additional comments.



In those files, the moves are ranked from best to worst (which may not be the most appropriate order for teaching purposes) ; to be precise, in a "Black to play and kill" problem, the first black move shown (the highest in the tree) is the right answer, and the second (just below it, therefore) will perhaps kill only by ko, while white answers (all failing to live) will be ranked according to the resistance they offer (forcing Black to find harder tesujis, or longer sequences) ; it could be helpful to read also some of the remarks in the annex. An example will allow the reader to compare both approaches : I could only give three diagrams, covering only one variation, of the solution of problem I.3.8 (a quite artificial double ishinoshita), where the sgf file shows a dozen lines of play, moreover much easier to follow that way...



To conclude, the diligent reader will probably best enjoy those problems by trying first to solve them without any help, then by having a look at the solution diagrams, and last by exploring the variations of the sgf files ; I tried to be there as exhaustive as possible (except for the most difficult problems), so if you still find something unclear (or perhaps wrong), do not hesitate to write (at )...



For many years, I have shown some of those positions to every interested player I could catch (and to many others ) ; I was often disappointed to see that, far from trying quietly to solve my beautiful problems for themselves, some of them insisted on putting their hands (and their stones) on my positions. For those troublemakers, I constructed the problem below, which no one has yet dared to disturb physically with his tries, and which will therefore make a fitting (and personal) introduction to this collection...







Appetizer : Black to play ; status ?

(click here for an sgf file of the solution)







Solution (1) : the first moves are not surprising...

Solution (2) (9 at 5, 10 at 3) : Black lives in indirect ko (mannenko)

I. Extraordinary life and death problems.





Problems in this first section are classed by themes ; one of their common features is the exceptional rarity (to say the least) of most of those themes in actual games (except for the problems of section 6)... First, let's look at some symetrical positions, trying not to disturb them (as suggested by the proverb telling to play on the axis of symetry) ; it must be admitted they are not all about matters of life and death...



1. Symmetrical problems







Solution 1 : the key move at 1 (an "off-limits" move)

is a probe opening two doors ; if instead one simply pushes ...





Black finds herself short of liberties (14 above 5)





Solution 2 : Phase 1 : threats of ladders

(I will let you look for them ; actually, there exists a Japanese version of this problem where they are constructed to be as tortuous as those of section III )

Phase 2 : first line footwork

(note the partial breaking of the symetry, perhaps unnecessary ; the theme appears at last, as 39 is a decisive double threat)



Solution 3 :

1 is the only move preventing a ko fight



Solution 4 : move 1 is necessary to prevent White

from escaping on the 2nd line





Solution 5 : nothing else prevents shortage of liberties

Solution 6 : move 1 threatens the two cuts

Problem 1 : Black to play and kill

(click here for an sgf file of the solution)



This is a kind of sacrifice, but a very short-lived one... They are not always easy to anticipate, as shown by the nice problem 1, from a recent Chinese beginners' collection (yes, their beginners are not made of the same stuff as ours...)







Solution 1



The "slow" key is hard to find (it is almost an "off-topic" move), especially if you have never seen the subsequent snapback combination ; below the 3k level, players often are lured by similar invisible snapbacks. You could have sworn that, after 2, the white group had three eyes and no weaknesses, didn't it ?







Solution 2 (7 at 5)

Solution 3 (9 at 1, 11 at 7)

Solution 4a (8 at 5)

Solution 4b



Problem 5 : White to play and live

(click here for an sgf file of the solution)

Solution 5 : White cannot do better than live in seki, else...

... he stumbles into a "parallel" double snapback



Solution 6 (beware of the order of moves)

Solution 7







Solution 8 : this splendid "parallel" double snapback

kills without ko ...

Variation : it was not easy to see how to prevent this ko...



Solution 9 (24 at 19, 27 at 15) : note the "slow" move 21

A variation without snapbacks, but with an elaborated twist on thieves' play (23 at 15, 24 at 17, 29 right of 27) ; White can in fact resist with yoseko, by playing 24 at 31, but ...



Solution 1 (6 at 4, 8 left of 4)

Solution 2 (5 above 1)

Solution 3 (6 at 4, 7 below 4, 8 at 4,

9 right of 4)







Solution 4 (7 at 3, 11 above 1)

Solution 5 : first, an unusual sacrifice

(it will reappear in the next subsection)

Solution 5 (follow-up)

(8 at 6, 9 at 4, 12 at 6, 13 right of 6)



Problem 6 : a natural position ; what is the best yose for White (and what is its value)?

(click here for an sgf file of the solution)



Solution 6 : because of the under-the-stones resistance (11 to the left of 2), White only gets 3 points more than by playing the hane at 8 ; on the other hand, if Black misses it and answers meekly at 4, the cut gets 9 points more than the hane (but is gote)



Solution 7a

Solution 7b

Solution 7c (17 at 11, 18 at 13)





Solution 8a (7 left of 2)

Solution 8b

Solution 8c



Solution 9a

Solution 9b (13 left of 10, 14 left of 13, 15 left of 12)

Solution 9c (29 at 23) Click here for an animated solution

Problem 10 (another highly artificial one) : Black to play, status?

(click here for an sgf file of the solution)



An incredible sequence of turnarounds ...







Solution 10 : first surprise...





Second surprise : Black declines the ko fight ...

... and kills without ko





To conclude this part of the section, here is, I think, the most astonishing ishinoshita played in a real game (or so did our master tell us). Actually, it is quite possible that this position (shown to us by Lim Yoo Jong, but coming, after some modifications, from the Xuan Xuan Qi Jing, where it is called Golden Cicada Casting Off Its Shell) was in fact "improved" from something really played (many "urban legends" of go (or weiqi) lore are of this type, for instance the one of Dosaku's tesuji). Anyway, the (hard to believe) story Lim told us was that in the position on the right, White, fighting for an important outside ko (not shown here) had deliberately ignored the ko threat (the triangled stone) and filled the ko, reading the resurrection of his group in another ko, and the fact that Black would not have any further threats. The solution given below is perhaps also not completely correct (see the annex for more remarks on this), and I let the diligent reader decide, for instance, if move 14 is really necessary, or is just losing some yose...





Problem 11 (from a real game ?) : could White really afford to ignore the ko threat ?

(click here for an sgf file of the solution)







Solution 11 : after the best resistance at 7 (in the other variation, 7 at 8, White get an easier-to-spot ko, but it is a two-step one, actually better for Black that the one of the "solution" : 7, 24, 11, 10, 21...), it ends with an under-the-stones tesuji (23 at 21, 25 at 7, 26 at 17, 27 at 13) ...

...and Black must find the first ko threat to take back 28 (if she connects at 29 as shown above, 31 takes back the ko to the right of 28, but 32 captures all the stones unconditionally) ; moreover, 30 is an intrinsic ko threat.

In the thematic example at left (where a liberty at a is necessary, a fact which was brought to my attention by Pierre Colmez), there is only a threat of under-the-stones play ; we will see another nice example with problem II.2.7, but there it will not be the main theme. Problem 13 is the strangest example I know of this idea ; I found it in a tesuji dictionnary compiled by Fujisawa Hideyuki (better known as Fujisawa Shuko, as explained in this article of Sensei's Library), amongst much easier problems, and it could also appear in my section on traps for professionals : some 4 dan pros have fallen for it (the trap is that it looks hard enough, so, after discovering the virtual ishinoshita, it seems solved, even more so if the amateur player who shows it to you looks harmless...)







Solution 12 (the thematic manoeuvre) : 4 captures (left of 1), 6 (above 1) is forced.

Solution 13 (10 left of 3) : White lives in ko

Variation 13 (6 at 4, 7 at 2): If White tries for unconditional life, he dies without ko !



Solution 1 : the 5-stones-in-a-row capture is not enough to live...

... as shown here, so White had better play 2 at 3, for a ko





Solution 2 (8 at 6, 9 at the centre of the T-shape) : Black can decline to

play the ko (right of 4), as the 6-stone capture is not enough to live...

In this easier variation, White loses the race by one liberty.



Solution 3 (1 connects, then Black sacrifices the 4 stones) : after 5, it becomes clear there is no way to form the second eye

Solution 4a (4 at 11) : after capture, Black plays back at 11 ; I let you finish, using diagram 4b...





Solution 4b (4 at 9) : same shape, on the other side





Another little-known situation is the sacrifice of a L-shaped string of four stones, when the return strike at the vital point not only reduces the shape to one eye, but does it in sente, as it threatens a snap-back.





Problem 5 appears in another Chinese training collection (designed for more advanced players, it must be said) and you should be quite strong to kill without ko were you not given the nakade hint ; problem 6 is a famous one from Xuan Xuan Qi Jing, with a shape similar to the one in the previous section but not looking so hard, except that it is full of traps, including the temptation of the same nakade. Studying it again after all those years, I discovered to my own surprise the "improved" variation 7, where the theme is no longer virtual...







Solution 5 : after capture...

...playing at the vital point threatens a snap-back

Solution 6 : after the atari at 10,

Black must resort to ishinoshita tactics

(13 right of 3), else...

...the vital point proves lethal

Solution 7 : now, Black can no longer

connect (left of 9)...

...and is killed by the nakade



Solution 8





Capturing 7 stones is not enough to live





Solution 9 (9 at 6, filling his own eye)

Capturing 7 stones is not enough to live



Problem 10 : Black to play and kill.

(click here for an sgf file of the solution) In problem 10, one of the largest centre nakade shapes, you will perhaps notice that the group of problem 1.1 even when it doesn't succeed in escaping, is without doubt quite tenacious ; actually, even if Black doesn't find move 3, life for White is not so easy to achieve, as will be seen in the joint sgf file...

Solution 10 (4 at 2) : The 14 stones capture isn't enough to live

UPDATE ! (15/11/2009)



The solution above is, of course, barely readable ; so, if your eyes get tired, you will probably be grateful to click here for an animated solution, or for the associated sgf file ; it is also displayed, in a more detailed version, on the site of GoProblems, but their solution doesn't mention all variations ; for instance, I owe to Motoki Noguchi the sequence showing that the last sacrifice of 6 stones in the NW corner is actually necessary. On the other hand, the solution I give (in the associated sgf file) of the Genran problem, is all mine, which could explain some of its defects...





The first one (problem 1) gave its title to Nakayama's book "The treasure chest enigma". I had lost the book, and it seems to figure nowhere on the Web (Didier Hallepée, one reader of the first draft, was kind enough to send it to me) ; I had composed a variant with some mistakes (now corrected), which were found by Didier Hallepée and Pierre Colmez, but I don't know if it is as difficult as the original problem (I suspect it is, as Pierre and I already fell into many traps while solving it ... ). The blind spot seems here to be Black's damezumari in problem 1 (curiously hard to see in this unusual shape) ; trying to solve it (without putting stones on the board, of course), professionals (and strong amateurs) forget this "detail", where weaker players don't encounter any special trouble.







Solution 1 : Now, at last, you should see why it is Black who is dead...



Solution of the variant : White dies for the same reason







This way too ...







Starting this way, the best White defence leads to a ko

(while we are at it, did you see what role the 1-1 stone played?)







The curious problem 3 has tricked many pros (including Yi Ch'ang-ho) ; there again, the theme is so surprising, and so unlikely to be found in a game, that they get carried away by their reflexes, and miss (or more precisely bypass) the solution, which is yet not so hard for weaker players...







Solution 3 : if Black stops playing at this point, she lives (in seki), but adding one more move is suicidal ! By the way, this seki is so unusual that the (old) Ing rules could not decide its value for Black (2 points ?), but anyway, they were modified after V.Gurvitch discovered the other strange sekis we will see in section IV...



Solution 1 : variation 1 (if White 4 at 11,

Black pushes left of 3, and the L-group is dead)

Variation 2 (this defence is the hardest to refute ;

if White 6 at 7, it reverts to variation 1)

Variation 3 (easier)



Solution 2 : the traditional answer :

White lives (in seki)...

... is in fact wrong : Black can get an indirect ko (mannenko)

after the "slow" tesuji 3 (another blind spot)



Solution 3a : White still lives (in seki, without any ko)... ...

Solution 3b : ... against all black tries...

Solution 3c : ... even this one.



Solution 4

(dead by "bent four in the corner")

Solution 5 : idem

Solution 6a : mannenko

(or ten-thousand year ko, or permanent ko, the later being my own translation)

Solution 6b : another very indirect ko (9 at 6)

Problem 7 : Black to play and kill the white stone

(click here for an sgf file of the solution)



Death of the white sansan facing enough black influence is a little known fact, one of the reasons being that the way to kill is not obvious : experiments show that, against a player giving you 4 handicap stones, his sansan will live more often than not... Moreover, it seems that pros recently found a way of living for White in the 9x9 square, which is the reason I only show here this problem in a smaller space...







Solution 7 : One must not get too close ; after these approaches, the L-group is dead ...



Back to the table of contents



Most difficult classical problems



To end this first part with fireworks, here is a selection of very hard (and beautiful) classical problems. Dosetsu's problem apart, it may be that your mileage differ (I will consider similar questions again in the appendix) ; the problem of how to play optimally starting from an empty board is usually perceived as a quite tough one too...







Solution 1 (9 at 7, 10 at 5)

This alternative solution (7 at 3) could explain

the bamboo joint in the variant

Problem 2 (a serious contender for the throne) : White to play, status ?

(click here for an sgf file of the solution)



There are other quite difficult problems in Xuan Xuan Qi Jing, for instance the one above, with its innocent-looking shape, but whose solution (by Japanese rules, a draw by repetition) is almost impossible to guess (not least because the first six moves get harder and harder to find) : Haruyama Isamu, one of the best pro tsumego experts, confesses to having spent six hours solving it (without putting stones on the board, of course) and believes no amateur would ever succeed, were he to spend weeks or even months on it ...







Solution 3 (15 at 7) : a "superko" (chosei)







Solution 3 : Phase 1 : a multi-stage ko is created (10 at 8)

Phase 2 : destruction and recreation of ko threats (18 at 12, 20 at 8)



Phase 3 : Black appears to have escaped... (28 at 12, 31 at 25, 32 at 26, 33 at 24, 34 at 12, 36 at 8, 38 at 26)

Phase 4 : last struggles (65 at 59, 66 at 61, 68 at 59, 77 at 72) , but more complicated variations are possible with the marked stone in place

As I said above, the net at 53 looks like a simpler way to catch Black ; this is the reason for the marked stone (left of 55) in the variant, which I believed prevents any simpler capture sequence than the one shown and doesn't hinder that one; the reader will see my analysis (of 2009) in the accompanying sgf file; it had been partially checked by Motoki, but I was still discovering new variations in 2009. If all this was correct (it was not : in 2010, Fan Hui discovered another weakness in those analysis), I could proudly present the problem with an "improved" caption : "This problem has been found on an old torn manuscript, with the information 'White to play and kill' ; what was the size of the go board ?", as you may now notice that Black escapes on any other size than the standard 19×19...



But in the summer of 2009 at the EGC (in Groningen), a suggestion which I had believed for so many years to be a urban legend (of British origin) reappeared : why should not Black push once more on the first line, for instance by playing two consecutive ko threats ?. This preposterous idea (which White cannot counter by declining to play the ko in the normal way too, as he need his threats to reduce Black liberties) had apparently been missed by everybody : one must recall that this exact sequence was explicitly refered to by Go Seigen and Kitani Minoru, during one of their famous games (Kitani was using a two-step ko to play devastating yose on the first line, and Go Seigen muttered "Xuanxuan Qijing", to the merriment of his opponent). It demolishes the original problem (Black succeeds in getting close enough to the corner to live there) and my pretty variations, but, with the help of Fan Hui, I was able to save most of it, by the following variant, which I now believe to be the only legitimate heir to the emperor :



