why do tsumegos have exactly one solution?

[Bill Spight]

$$B white to play and kill
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X X X X X X X O . O . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Click Here To Show Diagram Code

[go]$$B white to play and kill
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O X X X X X X X O . O . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

The only unique attack is on the point of symmetry.

$$W Only one eye
$$ +---------------------------------------+
$$ | . . . . . . 2 . 3 1 5 . 4 . . . . . . |
$$ | . . . O . O X X X X X X X O . O . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Click Here To Show Diagram Code

[go]$$W Only one eye
$$ +---------------------------------------+
$$ | . . . . . . 2 . 3 1 5 . 4 . . . . . . |
$$ | . . . O . O X X X X X X X O . O . . . |
$$ | . . . . . O O O O O O O O O . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

keeps Black from making two eyes. But Black can guarantee seki.

[Go_Japan]

Some creators of tsumego problems seem to think that each problem must have exactly one correct first move to be called a "problem" in their opinion.

When I create tsumego problems, they can have zero, one, several or (rarely) all correct first moves because this agrees to the reality in our games. The uncertainty about the number of correct first moves increases the difficulty of solving them on average.

If there always is a solution, then the case of zero correct first moves is not trained at all - bad! Even the classics admitted this by providing (only?) one infamous problem with tenuki / pass / ko threat being the only correct first moves.

Internetgoschool.com run by Guo Juan also does this. Basically, she presents real games for problems, so there are in her view "best" moves, but also cases where several moves work the same or where there is no local play and the correct play is to tenuki. I think that is much better way to study than always playing where there is one solution. As RobertJasiek said, in games, there are many times with multiple plays and sometimes with no solution to a local position and tenuki is best. This is especially important not to remove any potential aji for later in the game.

[Calvin Clark]

I think it depends on the author, the purpose of the problem and the context. Having only one correct solution helps a lot with self-study, whether or not you look at answers. The answer book can be shorter, too, so it's a convenience to authors.

But there are other ways. Mingjiu Jiang 7p presents his students with problems on the board and asks them: "first tell me the result." They are not supposed to just start putting down stones to see what happens. So the exchange frequently goes like this:

Mingjiu: First, tell Ame the result.
Student: I think black can kill.
Mingjiu: Okay, how many ways can black kill?
Student: Uh....

Then at some point if you do put down stones and you're not sure, you have to deal with the man himself. This is interactive teaching. He sometimes encouraged students to work together when studying problems, so they see more counters and refutations. He has a point. If you study alone, it's easy to get into the habit of optimistic reading.

In that style, often there was more than one solution and maybe one was really best all the time or maybe which one is is best would depend on the whole board position, just like in real games. I think it is good way, in the same way that fine wine is good. But few can live off of wine, so the water of conveniently contrived closed positions will have sustain us most of the time.

[goPlayerJuggler]

Yesterday I started a discussion related to this on SL, because most of the tsumego there with multiple solutions have been marked as "unsound", which I don't really like.
https://senseis.xmp.net/?topic=15325

There's a reply from Unkx80 which I'd like to share here:

in both Chinese and Japanese, there is a specific term for failed life-and-death problem constructions: 失题 (Simplified Chinese) / 失題 (Traditional Chinese/Japanese), literally "missed problem". This term is used when a problem has either (i) no solutions, or (ii) more than one solution.

In printed Chinese problem books, it is common to see a statement on the problem itself stating that "this is a "missed problem" with two solutions". I suppose this is the same for Japanese - I don't know the history, but I have a feeling that the Chinese Go community had imported the "missed problem" concept from the Japanese.

So my issue on SL seems to be, at least partly, an issue with terminology/translation from Chinese & Japanese; or a difference in Go culture between "Asia" and "non-Asia".

[kvasir]

Tsumego doesn't have to have exactly one solution. There are many examples of problem collections that don't follow this pattern. That there are books, as was suggested, that will label such problems is evidence.

It is a matter of perspective if you wish to call problems that don't have any or have many good solutions "inconsistent", "abnormal", "unsound", "different", "missed" or something else. Though it does seem a bit pedantic to myself if the problem isn't otherwise unclear. Unclear tsumego can be infuriating though.

[John Fairbairn]

Yesterday I started a discussion related to this on SL, because most of the tsumego there with multiple solutions have been marked as "unsound", which I don't really like.

I think you are right to dislike it. In fact, on the assumption that the problems marked "unsound" were classical problems - which seems likely, given copyright considerations - it is unsound to mark them unsound. It overlooks why the problems were devised in the first place.

I have discussed this at some length in Volume 1 of the Encyclopaedia of Classical Go Problems. The gist of my argument, which is backed with quotations from writers of the time, is that problems then were for recreation with friends. They were topics of conversation. In the absence of television and the like, and even for much of the time a lack of access to books, go problems and new books were seen as objets d'art, to be pored over lovingly and discussed. The more multiple solutions there were, the more to discuss. Almost all problems had allusive names, which provided clues, either for solving or memorisation, but which had intellectual overtones that further stimulated discussion.

This way of viewing problems as part of parties for friends lasted for centuries. In the Ming dynasty, it became more formal with the formation of yuan she, which can be considered a bit more like European salons. Friends were invited as before, discussions took place as before. The new element was some emphasis now on introducing new talent from outside, perhaps with an element of sponsorship. Go masters certainly were part of the new talent invited to the "salons."

Some of these new masters made a name for themselves by pointing out extra lines, or sometimes mistakes, in old problems, and their new variations were typically inserted in new editions. But they never used words like "unsound" or reductio ad absurdum to one line. It was all about adding grist to the mill.

There is one problem I looked at recently (part of Volume 2) which went on for (from memory) 31 moves, whereupon Black was found to be dead (unexpectedly, of course). It was a kaleidoscope of themes. That one problem would have provided entertainment for a whole evening on its own. Some later master pointed out that Black could have made a ko on move 4. True, and most amateurs would have seen that as a possibility anyway. But for Black to play a ko on move could only be justified truly if he had been able to see ahead to move 31 and realised he was actually dead without the ko.

The old collections were never a set of drills to be practised while commuting in your sedan chair on the way to the next court session. The collections were almost totally disorganised. They mixed hard (often VERY hard) and easy, "X to kill" along with "Y to live", and alongside many "what is the status" problems. Life & death were mixed up with tesuji problems and boundary-problems. Also on the mix were pure conveersation pieces such as triple kos. The nearest you get to orderly categorisation is grouping together a few problems which relate to, say, fish or which, for example, all quotations from The Records of the Grand Historian.

To reduce such complex and facinating collections to exercise drills with one solution is pure bowdlerisation.

That is not to say that collections with one-solution problems don't have a place. But they are part of the dumbing-down and fast-food culture of the modern age. Yet, if you judge them by their effectiveness, you could easily argue they don't have a place, really. Almost all modern tsumego collections are the equivalent of learning to dance by watching Avantgardey videos. Those who really want to dance artistically go to schools like the Vaganova Academy, The Royal Ballet School, New York City Ballet, the Paris Opera School, etc. etc. And guess what - all these schools concentrate on classical technique.

[unkx80]

Yesterday I started a discussion related to this on SL, because most of the tsumego there with multiple solutions have been marked as "unsound", which I don't really like.
https://senseis.xmp.net/?topic=15325

There's a reply from Unkx80 which I'd like to share here:

in both Chinese and Japanese, there is a specific term for failed life-and-death problem constructions: 失题 (Simplified Chinese) / 失題 (Traditional Chinese/Japanese), literally "missed problem". This term is used when a problem has either (i) no solutions, or (ii) more than one solution.

In printed Chinese problem books, it is common to see a statement on the problem itself stating that "this is a "missed problem" with two solutions". I suppose this is the same for Japanese - I don't know the history, but I have a feeling that the Chinese Go community had imported the "missed problem" concept from the Japanese.

So my issue on SL seems to be, at least partly, an issue with terminology/translation from Chinese & Japanese; or a difference in Go culture between "Asia" and "non-Asia".

So this discussion spread over to Life in 19x19 because of a lack of responses on Sensei's Library. Personally I have little involvement with Go for over ten years, so take what I say with a large grain of salt. But nonetheless, I think some context needs to be set here.

As far as I can tell, the marking of problems on Sensei's Library as "unsound" is all done by one single user, who is currently very active. On his homepage, he says that he is a Japanese dan player, and English is not his first language. I think these are important points for consideration.

I am of Chinese descent and I don't know the Japanese language. But nonetheless I make the following comments:

• It is evident to me that this user used the term "unsound" to mean 失題 or "missed problem". However, I feel that the term "unsound" might be nuanced somewhat differently compared to 失題; somehow "unsound" seems overly strong. I suppose those who know the Japanese context may want to correct me. But I haven't thought of a short and sweet English term to capture the same idea in a neutral tone either.
• I suspect that 失題 is more of a Japanese culture rather than Asian wide. As far as I know, the Chinese-speaking Go community don't demand life-and-death problems to have unique solutions as much as the Japanese counterparts.
• In my opinion, exactly what is meant by "uniqueness" of a problem is actually ambiguous. In a symmetrical problem, often it is permissible to start from either side. In a problem involving a capturing race, the order of taking liberties often doesn't matter. The Japanese seem to accept such sources of "non-uniqueness" and don't seem to label such problems as 失題 either.
• If this page is typical of where they draw their line on what is considered 失題 (diagram 8 is 失題 because diagram 9 is also a solution, therefore the problem construction should be amended to diagram 10), then personally I find it rather extreme and I don't really share this opinion. After all, real games aren't as clean as constructed life-and-death problems. But obviously the Japanese bar for 失題 is very high.
• On the other hand, if I construct a problem with a main line in mind, and it turns out that it has a very much easier solution, then I would not have met my objective for constructing this problem. Therefore I share the same sentiment as described in this article (based on Google translate, a professional player was visibly disappointed when his problem had two solutions).

Sensei's Library has existed for two decades without problems being marked as "unsound", and of course I have no complaints. goPlayerJuggler didn't quote my entire response on Sensei's Library, but I also effectively stated that I kind of understand where that Japanese user was coming from and I condone his actions, and therefore I make no stand on this issue. If anything else, perhaps the term "unsound" should be changed to something more neutral sounding.

----

On the topic of unique solutions, it is interesting to compare Go with Sudoku. Both are games that were exported from Japan to the rest of the world. Like Go problems, the Japanese always construct Sudoku puzzles to have one unique solution, and I believe the main reason is that Sudoku puzzles should be solvable by logic rather than guessing digits in cells. Unlike Go, the English speaking Sudoku community seems to have accepted the requirement for puzzles to have unique solutions, albeit somewhat grudgingly. In fact, it has been proven that a valid Sudoku puzzle must have at least 17 givens, anything less the puzzle will have at least two solutions.

[Knotwilg]

----

On the topic of unique solutions, it is interesting to compare Go with Sudoku. Both are games that were exported from Japan to the rest of the world. Like Go problems, the Japanese always construct Sudoku puzzles to have one unique solution, and I believe the main reason is that Sudoku puzzles should be solvable by logic rather than guessing digits in cells. Unlike Go, the English speaking Sudoku community seems to have accepted the requirement for puzzles to have unique solutions, albeit somewhat grudgingly. In fact, it has been proven that a valid Sudoku puzzle must have at least 17 givens, anything less the puzzle will have at least two solutions.

I have used uniqueness as a solving device. If I have 3 boxes with duplets (e.g. 2 & 7 are the only possibilities) forming a potential rectangle, then the 4th box in that rectangle can't be a 2/7 duplet, or there would be 2 solutions. It never felt right as a device but it also didn't feel wrong. Fuzzy logic.

OT: If "unsound" troubles readers - and I understand why it does - I'm willing to temporarily halt it.

[jts]

Whether or not "unsound" is the right translation, I think it does make sense for SL to adhere to the one-first-move convention, at the very least for the tsumego intended to be seen by beginners. Around 2010, didn't SL have a number of invalid user-submitted tsumego that had to be (eventually) fixed or removed?
Non-standard problems seem to make errors much more likely and validating problems more of a time-sink.

[RobertJasiek]

does make sense for SL to adhere to the one-first-move convention

Disagree.

Non-standard problems seem to make errors much more likely and validating problems more of a time-sink.

Disagree to the PR tag "non-standard".

Problems with 0 or several correct first moves require correctness as much as problems with 1 correct first move. However much time is needed must be invested. If a problem is too difficult for a writer, its posting can be delayed until solved rather than expecting SL to be a problem solving service by everybody else.

[John Fairbairn]

I infer from the comments so far that there are two distinct issues here.

What I understand when people say a solution is "unsound" is that it is incorrect. In modern problems, this usually when a deviser claims Black can kill White but some later person comes along and shows that White can live or make a ko. "Unsound" is a reasonable word in such cases, and the mistakes should be pointed out.

In classical problems, the deviser does not say (in the published version) that Black is to kill (or whatever). He just presents the problem and shows what he regards as the most interesting, entertaining, beautiful or useful line. As I have already said, the problem is a "topic of conversation." It is like coffee-table book. That is not to say there are no unsound problems in the classical canon, but some of the so-called corrections claimed are just hot air. It beggars belief to claim that an ancient master who can present a 45-move problem that contains under the stones, a bent elbow, a tombstone tesuji and a remote L connection all in one problem could not see a 25-kyu ko. (But I repeat again, it's really only a 25-kyu ko if you can read all 45 moves of the fancy solution so that you know a ko is not just possible but necessary).

But the other interpretation some people adhere to is that there must be a single unique first move.

I personally have never come across this as a requirement in CJK works, but I can well believe it exists somewhere, simply because it exists in chess, at least for the Sam Lloyd type of problems. In my experience, these problems are beloved by mathematicians who prize "elegance". Knotwilg appears to confirm that the same sort of thinking is prevalent in sudoku. I can see why that might appeal on aesthetic grounds, though I don't share the admiration for the results. A possible explanation for the popularity of hat type of chess problem is that it was the easiest/cheapest way to present chess in a newspaper chess column.

But when we are talking about life & death problems in go, surely we are nearly always talking about doing problems in order to make you a stronger go player.

If that is the goal, you need to do problems that train your intuition (the database in your brain) and help you read deeper or faster. What on earth does limiting a problem to only one line ha ve to do with that?

I can see situation where an author writes a book on, say, how to kill with hane + nakade. Every problem revolves round that theme. Clearly, if a particular problem could be solved more easily or more clearly with, say, a tombstone tesuji, that may take some of the presentational gloss off his book. But it doesn't actually make his problem unsound.

The other big drawback with assuming that only one move works in typical life & death situations is that once you've found a workable solution you stop. That's not complete failure, but it does mean you are not adding everything you could to your intuition or developing the breadth as well as the depth of your reading. And in real games you need to know not just whether a certain move kills or which it end up as mochikomi or ajikeshi. You need to know whether living with two eyes in gote is better than seki in sente or vice versa.

I see a similar drawback in what seems to be the standard ways to measure study of L&D problems: "I scored 98 out of 100" or "I took no more than 20 seconds for each problem." But these people are measuring the wrong things. They are just measuring spotting the putative first move. It's not a complete waste of time, but it's nothing like as efficient as learning things like what conditions must exist for the rooster on one leg to work and then memorising (i.e. putting into the intuition database) those specific shapes.

The classical collections seem to me to be better suited to more well-rounded study. It's not especially easy of course. Old Chinese literature is full of examples of people who explain their prowess at something by saying "after X years I learned to...". The include COnfucius, or course, but there are famous examples such as Zhuang Zi's cook Ding, who learned "after three years" to cut up a carcass without snagging his knife on ligaments and tendons. They are just expressing in their one fashion what we are taking about when we say "10,000 hours" There's nothing new under the sun.

And that includes granny's wisdom. Since I have just mentioned butchering, one of the most apposite of her saws may be: "There's more than one way to skin a cat."

[Kirby]

Go problems sometimes have multiple solutions. Seems fine to me.

[kyulearner]

In the Japanese go community, Tsumego are differentiated from life and death problems and are thought as puzzles intended to train reading ability. The preferred way to solve them is to find one correct line of solution and to refute all other incorrect moves. Therefore the problems themselves are required to be structured in such a way.
However, it is too difficult to put together such problems every time, so tsumego magazines (published in 20th century and non existent now) required one correct move for the first move only, and turned a blind eye to multiple correct moves from the third move onward. As for other factors a not placing a stone non related to a solution, or that a capturing race end in a exactly one liberty difference were upheld by tsumego writer pros such as late Maeda Chinji 9p, who described otherwise tsumego problems as "ugly", and such thought is inherited to present tsumego writers.

[kvasir]

It is Maeda Nobuaki, not Chinji, right?

That people have adapted various conventions, to suit their own aesthetic sense or for other purpose, could be seen as evidence that tsumego doesn't have to be one way or the other. Lot of tsumego does, however, have one and only one solution and I think it is possible to look for better explanations for this fact, something other than cultural imperatives.

What about the fact that many classical collections of tsumego didn't even come with solutions? That wouldn't appear to put the emphasis on the number or quality of the solutions. While it would probably be a good convention for most tsumego to have one and only one clear solution but isn't it backwards to insist, maybe centuries later, that the solutions absolutely have to be one way or the other?