How many unique tsumego problems are there?

[quantumf]

Ignoring direct copies, and ignoring rotational copies, how many unique life and death tsumego problems do you think exist? Obviously new ones get created all the time, so I'm looking for a rough order of magnitude. Some kind of justification for your estimate would be nice.

For instance, if we assume there are 500 tsumego books, with on average 200 problems in each, and with a 25% copy rate, that gives a figure of 75,000 unique problems. Each of those three numbers is a complete guess.

[skydyr]

If you have a problem in a corner, relying on the surrounded group having one extra liberty free, does changing the location of that liberty make a new problem, or not?

Are problems 3 moves in from a previous problem new problems or not?

Are wrong variations (or right ones with different resistance) new problems, or not?

It's not clear to me what the right answer is to these questions. Certainly they could be considered problems for a certain strength of player but just variations for a stronger one.

[quantumf]

Problems that are composed of other problems I would regard as new problems. In other words, if two of the branches of the solution are effectively simpler (but presumably different) problems, then the new problem is a valid new problem.

Shifting the liberty doesn't strike me as a new problem, but that might depend on the location of the liberty - moving the liberty may require a different set of variations to be analyzed. Maybe we need to see some examples.

[DrStraw]

For all practical purposes there is an infine number of tsumego problems. How many of them have ever been written down and published is a different matter. I find it hard to believe that it could be less than six figures with all the print and online resources these days but I doubt anyone can really give a estimate with an decent expection of accuracy.

[skydyr]

For all practical purposes there is an infine number of tsumego problems. How many of them have ever been written down and published is a different matter. I find it hard to believe that it could be less than six figures with all the print and online resources these days but I doubt anyone can really give a estimate with an decent expection of accuracy.

I expect there are probably on the order of 5-10k "simple" problems, maybe less, by which I mean problems exploring somewhat standard corner and side shapes, like 7 in a row on the 2nd line, the various L and J groups, the tripod group, the door group, nakade in the center of three, etc. To answer my own question, I wouldn't consider a liberty location change significant unless it requires the analysis of different variations. Variations with the various legs, hanes, angle stones missing leading to false eyes, etc. are fair game. I'm also limiting this to life and death, as opposed to standard tesuji problems that may involve capturing and saving stones. For reference, the collection of problems from Cho Chikun's life and death encyclopedia is in the neighborhood of 2500.

Once you get into more complicated and less standard shapes, or ladder problems, or tesuji, the configuration of stones can be a lot more varied to create the problem, making it much larger and harder to count. In a sense, practically any whole board diagram could be considered a problem, black (or white) to play and win/keep the game in balance/complicate/capture etc.

[quantumf]

Sure, the possibilities are infinite, but since any potential problem has to be carefully analyzed for correctness, it presumably gets exponentially more difficult to verify this the more complex the problem is. So I don't think there are thousands being generated every day. I don't even think hundreds are being generated every year.

I would confine the search space to corner or side life and death problems.

I hear anecdotally of insei's solving "all" the life and death problems out there. Presumably they mean they've solved all the classic sets. Maybe that gives a different perspective to consider - all the plausible tesuji's, vital points and and reductions of eye space, and every plausible combination of the above. How many would that be?

[RobertJasiek]

Problems (reasonably) analysed for correctness and other than copied played full board game positions is a nice description for what can be considered tsumego (or similar) problems. How do I roughly estimate 200,000?

- 1,000 books each with 100 unique problems = 100,000.
- Other printed media and files = another 100,000.

It is easy to underestimate such numbers. E.g., although 2014 has been a "lazy" year, last year I have created 331 easily counted new problems and probably a couple more for specialised purposes.

[Uberdude]

Does this problem count? (I think it should).

http://www.lifein19x19.com/forum/viewto ... =15&t=5099

[Bill Spight]

Does this problem count? (I think it should).

http://www.lifein19x19.com/forum/viewto ... =15&t=5099

I agree.

Do we count these as the same problem?



I would.

[gowan]

There are "themes" of tsumego problems, as the two problems Bill posted have the same theme. I would say they are not "unique". If problems with the same theme are not considered different then we are really counting themes and that would drastically cut down the number of unique problems.

[skydyr]

There are "themes" of tsumego problems, as the two problems Bill posted have the same theme. I would say they are not "unique". If problems with the same theme are not considered different then we are really counting themes and that would drastically cut down the number of unique problems.

Taking the problem in the upper left as an example, what sorts of stones could be added or moved or removed to keep it the same problem as opposed to a different problem?

[quantumf]

It is easy to underestimate such numbers. E.g., although 2014 has been a "lazy" year, last year I have created 331 easily counted new problems and probably a couple more for specialised purposes.

Impressive, but unless you both own and actually check against all these 1000 problem books how can you be sure they are unique?

[jeromie]

I don't think Robert needs to be sure; he just needs to have reasonable justification for his assumptions. This seems like a classic Fermi problem; we're unlikely to have enough data to point to a real solution, so we're left with making educated guesses. Perhaps Robert can let us know if there was any data (besides his own experience) that led him to choose those numbers, though.

I'd have to do some basic research into the number of Asian language problem books before posing my own guess. I have absolutely no idea what's out there, and I'm guessing that's where the vast majority of the corpus resides.

[RobertJasiek]

quantumf, I guess 25% (order of magnitude) of my problems are standard shapes with standard problem questions. So, if you like, round down to ca. 250 last year. Since I invent the problems without looking up other problem sources and from having seen many problems, it is unlikely that a significantly greater fraction is not unique. For me, the difficulty is not inventing a problem but inventing such a problem fitting a particular topic and difficulty. This lets me occasionally run into a dead end of a too complex problem; after 2 wasted hours, I give up, discard the problem and instead invent a different problem.

jeromie, data for my own problems: I do not want to start another thread just to be allowed to state the data. Data for numbers of unique problems in books: I have seen a few thousand different books. Most were problem books. Nevertheless, the numbers 1000 and 100 are still wild guesses. OTOH, we can double check the order of magnitude. Surely, there must have been 33 diligent book problem creators in the history of go creating problems for 20+ years. Each of them must have created an amount of ca. 3000 new problems. E.g., Hashimoto Utaro was famous for creating a problem a day. Let him do so for decades and he alone would have created 10,000+. Were they published? I do not know.