This small guide is written for each player
|Table of contents|
Many times I hear questions and requests like "How can I become strong?" or "My Go lacks this or that. Please teach me how to be better at it!". In general, I think many people overestimate the role of a Go-Teacher. Of course, it's very important to play and analyze with stronger players too, but still the teacher is not everything. Most of the learning consists of exploring Go for yourself, and not by having every single move explained.
Actually, most part of my study in Japan did not consist of being taught by pros, but of studying by myself. One big point of being next to professionals was that they explained how to do this.
For you, these lines mean that you don't have to go to Japan or find a 6-Dan teacher to become incredibly strong!!! Instead, if you are ambitious, you just have to know what to do by yourself. This is why I decided to write this small tutorial.
Many people keep saying that Go is mainly about territory, and that Life and Death is just important for stubborn killers, who use Go to escape their own aggressions but never understood the real game. I believe this is rubbish!
At first, let me talk about Go-history and philosophy:
In ancient China, people were not scoring territory at all, but instead just the stones on the board. So originally, Go was about "gaining life for as many stones as possible" instead of territory. Building a territory - i.e. an area where no opponent's stones are able to live - was just one strategy to secure life for many stones later. In other words, Go was just about life & death! When the Japanese changed the rules to territory scoring as they found this more elegant than scoring stones, the rules of Go were cut apart from the original idea, which lead to the widespread misbelief among amateurs that Go would basically be about just fencing in points.
All professionals know better. Just recently Saijo Masataka 8p visited Hamburg, and while commenting on a game, he said: "In Fuseki and Middle Game, territory is not important, but strength and weakness of groups".
Now the five-hundred-million-dollar question: How to improve your judgement of weak and strong groups? Hint: Look at the Headline.
I think you are beginning to get the point. Be honest: How many of your last ten games were decided by just building territory, and how many of them by either killing stones or, if you are already a dan-player, by the implications of misjudging the strength of a group, for example being heavily attacked and therefore losing too many points by its implication?
There's maybe one more point to say: By doing much tsumego, your reading ability will increase in general, not just about life and death and tesuji. So you will have an easy time calculating endgame sequences and other stuff, so this will also be affected greatly by doing tsumego.
Right, this really happens sometimes with players who do tsumego the first time in life, as it is the first time they start to focus on strengths or weaknesses. But this is just an in-between stage and still an improvement compared to before, when weak groups were ignored by both players half of the game. It's ok for a while as you can try out and find the limits of your new knowledge. After losing enough games because of trying too hard, your way of dealing with weaknesses will become more subtle: You will create double threats of killing and making points, and you learn how to fight in a safe way that pays attention to both attack and defence. After really mastering life and death, many players suddenly change to a very calm, peaceful style, as they know when to avoid having a weak group and when to refrain from hard fighting since they can read out when it doesn't work.
For asian people, tsumego doesn't mean go problems in general, but especially life and death, and also problems about escape and capture rather than just building eyes. From my point of view, a mix of about 60% "real" life and death plus 40% escape and capture sounds nice.
There are three levels of difficulty that may appeal to you:
Lee Ki-Bong, Korean Go professor and 8 dan, recommends to do 1/3 of each type, but I believe that you should concentrate on the problems you enjoy most: If you like the feeling of having solved a problem, you can do problems that are not too hard for you, if you're looking for a challenge, try out harder ones (but don't spend more than 10 minutes at one time for one problem).
Now the most important thing:
Let me explain why: The right way of learning Go is to find new ideas yourself, instead of copying those of others. It won't help you improve, if you know one solution by copying. As you weren't able to find out alone, your reading ability is not yet good enough to understand the problem completely. Even if you know the solution, you don't know why it is right and why the other moves don't work, because you couldn't read out all variations. So even if you feel wiser, your reading didn't improve and the problem was useless.
If you are frustrated with not solving a problem, just continue with the next one without looking at the solution!
This is the right approach, used by all ambitious eastern students. Your reading already improved while trying to find out yourself, even if wasn't successful yet. Just do other problems to divert your mind from the unsolvable one. After a few more problems or after being through with the whole book (just as you like), you can have a second try with the problem, and maybe you can solve it this time. If not, continue in the same way until one day you made it! I can tell you, the satisfaction from finally having solved such a hard problem will be much bigger than your initial frustration, so you will be very motivated to do more.
After repeating a book two to three times, almost all of the problems will be very easy for you, and you can continue with a harder book. After you did the Chinese classical books, your reading ability is exactly like a pro's, and you should be able to rise to 7-8 dan. That's it!
Nowadays there's much tsumego available on the net, but I personally prefer printed media most of the time. Try both yourself and decide.
I believe that it's important not to submit to your teacher completely. Instead of just accepting everything he or she says, you should explain what you thought when you played, so both of you can compare his ideas with yours, and you can try to judge together whose were better. Of course, most of the time, the stronger player will be right, but sometimes he will not!
My teachers in Japan insisted that during analysis, there's no teacher and no student, but instead two equal partners who explain and compare their ideas, maybe even in a sort of fight/discussion if they disagree. In this way, all participants can learn from the game, though usually the weaker player of course gets more from it. But in this way there's a chance that he really understands instead of just copying blindly.
If you know a few more ambitious players in your town, maybe you should ask them to found a study group to meet like once a week to show and analyze each others games. This way all of you learn to get new ways of thinking and estimating, and as you are together you can try to decide which one fits best into a situation. It is said that the Korean and Chinese top-professionals are recently so much more successful than the Japanese because they are studying together, not alone.
Japanese pros recommend repeating and learning professional games (I had to do 100 when I was in Japan). By this you can get a nice feeling for flow and shape, and you find a lot of new ideas how to use your stones. On the other hand, most Koreans believe that before being around 7 dan, pro games are almost useless as you don't really understand most of it before you can read like a pro.
So you should find out yourself how many pro games you want to look at. It might also depend on your goal: If you want to win as much as possible, pro games don't help too much IMO. But if you see Go as an art, you will love the beauty of their play and it might help you finding elegance in your own games.
It's up to you, whether or not you want to do this. Just do what you enjoy!
But which games to look at?
Maybe you should concentrate on games of real top-players, as their Go is even more complete than other pros - and there are enough games, so why not choose the best of the best? There's much choice, from Shusaku to Lee Chang-Ho, Japanese, Chinese and Korean. All of them are very good, so you can decide what you like. If you like straightforward, understandable moves, you might prefer older Japanese games, i.e. Shusaku. If instead you love violent, chaotic fighting, you could chose some modern Korean stuff, i.e. Cho Hun-Hyun. Maybe you should try out very different games to find out what you like. Then you can start learning games of one or a few special player(s).
How to learn games?
Like with everything else in life, you must find your own way to do so. I can just give some proposals, but please feel free to adapt:
All of the time, focus your mind on these topics:
Also, always try to imagine where you would play in this situation and why. Then compare to what you believe the pro's aim was. Most of the time his idea is superior to yours, but not always. Don't think too hard to decide this, it's already great if you can get his idea.
One game alone probably won't affect your style too much, so if you are serious, give yourself a challenge like 50 or even 100 games - yes, it's possible if you're not too old.
At last, I give you one warning:
After you looked at some games, you will be tempted to copy pro moves blindly. That's a very bad idea, as it will lead you to play moves whose meaning you don't understand at all - this is not Go! Although it's useful to develop a good intuition for shapes, you should never forget the objective behind a move. I know what I'm talking about, and because I never heard a warning like this, I'm still fighting against this bad attitude. With this, learning pro games can even affect your Go negatively! So just make the same move the pro did after assuring that the idea behind it fits to the position on the board and thinking about alternatives.
In general, every minute you spend with Go will help you improve, so feel free to do everything you enjoy. But you should always be aware that successful home study consists of maybe 80% life and death, and you will realize that joseki and endgame also have a lot to do with it.
To talk about joseki, you know this proverb: "He who starts learning joseki will become three stones weaker". The meaning behind it is exactly like mentioned at the warning above: It tempts you to copy moves you don't really understand, which is a very bad habit. If instead, you replay joseki while always trying to find out why the moves are better than others, it can help you improve indeed, but before you can do so, you must be able to read very well.
Charles: One question. There must always be players who lose more than 50% of their games. Is this course of study enjoyable for them?
Benjamin: Sorry, I don't get your question at all. I mean, for statistical reasons, of course all of the time someone has a worse score than 50%, but do you think these will always be the same persons? Your score depends on your rank, so players with permanent bad score probably are ranked a bit too high, those with good scores too low. I don't understand what this math stuff has to do with the way people should study...
Charles: Well, I do wonder about this, for everyone. Maybe, for the fast-improving player who wishes to continue to improve fast.
Lop: I'm sure there are players who don't enjoy the methods Benjamin suggests. Although I don't think that it depends on their winning percentage. One can lose many games and still have fun studying tsumego. Anyway people who don't enjoy studying as Benjamin suggests should do something else they like better. Why should anybody do something he doesn't like? I'm certain that there are at least some players who appreciate Benjamins tips. No way of studying fits the personal preferences of every player.
Benjamin: What exactly do you you mean with "the method Benjamin suggests"? I don't think there are Go players who don't like to play, and not so much ambitious ones that don't want to analyze, so I think you're talking about tsumego. As I've written there, I know there are many people who don't enjoy tsumego right now, but as to my experience, once they really started with the right method, most of them start to love it - try it out yourself maybe...
Charles: As I understand it, there are basically two approaches, which one could call the Rob van Zeijst and Pieter Mioch styles. Van Zeijst would emphasise tsumego, while Mioch sees study of pro games as important. In a sense, I feel, the van Zeijst ideas tell you about necessary conditions (no one becomes really strong who is weak at life-and-death, endgame). Sufficient conditions are more interesting, to me; though obviously there aren't any: it is simply not the case that one can identify ways that guarantee progress. That is what I wanted to say first. If you have to rely on (i) opponents who actually know the important things and (ii) learning from analysing your games (very important) with others telling you what you need to know, then again these seem to be necessary conditions. Obviously my interest, from teaching a few hundred players, is more related to the articulation problem.
By the way, I thought a separate discussion page was a better idea. I'm sure Benjamin's ideas are interesting for everyone; my comments weren't meant to imply otherwise.
uXs: You say never to look at the solutions of the tsumego exercises. But then how do you know you found the correct solution ?
Niklaus: Easy, you are just not done with the problem until you are 100% sure that it is correct. Also, often the solution has got a certain elegance, which makes you recognize it. If you have to look at the solution to make sure, then you are probably wrong :)
Chris Hayashida: There is the danger that you find a wrong "correct" solution, though. I agree with not playing it out, but I think knowing about the pit falls of your wrong solution does help.
One thing I did, once I was stronger, was to re-read the Graded Go Problems for Beginners, and read out the solutions completely in my head. This included all of the variations I could see, as well as the life/death of the groups in question after the final position. It probably force you to read four or five moves beyond the solution, as well as a number of branches. I think it helped my reading, but possibly just because I was practicing reading more.
Robert Pauli: (Meta)
Benjamin: Dunno, what would you propose instead? Thought the subpage-thing would give a better separation about what I consider "my" pages and where I want to help creating normal wiki-pages (didn't know that subpages don't have separate discussion pages). Don't like it? Better ideas?
BramGo: I am amazed. When I read your page, I totally agreed on every item you mentioned. This page really is a nice job. And still so many negative comments?!?! About life and dead, the "not looking at the answers"-method is something I heard before. It's mentioned at the life and dead section on gobase for example. Also on sites like DashN it is impossible to look at the answers. So it is not like this is a crazy idea. I totally agree with Benjamin here.
Grauniad: The IGS Art Gallery Problems are published without solutions so you can't look at the solutions. These problem seem very difficult to this KGS 12k player - do they even have solutions? And if so, where? :-)
Rich: Thankyou for your advice, Benjamin. I must say, in addition to tsumego, I also found a big improvement on studying linking and splitting tesuji - this ultimately then comes down to the fact that your chances of surviving life and death (or inflicting it on an opponent) improves.
Do you have any recommendations for tsumego anthologies in the high-kyu/low-dan range? I'm somewhere around 5k and seem to be between a lot of the bigger collections. Also, it seems to me that most tsumego is based around corners, at which point 2-2 plays and so on become very atypical...
revo: I have a question about solving tsumego. I understand why it's important not to look at the solution, but as a weak player (15-18k), I always got the feeling that I didn't find the best answers of the opponent. So how can I be sure I solved a problem? If I killed white, maybe I just did it because I didn't see how white can stop me. Any suggestions?
Shaydwyrm: I have been trying to incorporate some of the advice that guides like this have to offer, and one conclusion that I have come to is this: if I'm not absolutely sure I found the best answers to my moves, then I haven't actually solved the problem, even if I found the moves given in the solution. The obvious followup question is, how can I ever be absolutely sure I've found the strongest resistance? My answer is to have read out every possible move. This can be extremely painful to go through, but to me it feels like the right kind of pain for improvement. First of all, as the problems get more and more difficult, this approach becomes more and more important - the more difficult problem sets are constructed so that moves that seem impossible at first glance become solutions, or tesuji to resist. Second of all, without developing that kind of tree-structured, thorough reading, I don't see how you can confidently play out a complicated life and death situation in a real game. Instinct for the vital points is useful, but it has to be backed up by good reading if you're going to be right 100% of the time. Finally, if it seems impossible to read out every single move, then perhaps the problems are too difficult to use this method at your level. I like to work with the most difficult problems that I can read out completely; when in doubt, I skip the problem and move on, and if this happens too often, I move to some easier problems.
nachtrabe: In Hapkido our Master Instructor used to say that "the price of knowledge is pain." There is a lot of truth to that.
Calvin: I have the same concern. But also I often find that I've refuted the strongest response but didn't see the weaker ones. Then if I look at the problem in more detail, I see that it's carefully designed so that the weaker one just barely doesn't work because there's an extra stone that might not be there in a real game position---it's just there to make the problem work. The question is: what's the hazard of deluding yourself into thinking you've solved problems you haven't solved? Maybe it's okay because the thing you are missing will later be required to solve tougher problems, so you'll learn it eventually, or maybe carrying the wrong answer in your head isn't so bad because the exact problem is not likely to come up in games. But some will. For a long time as a beginner I thought that a rectangular six eye shape was alive. Unconditionally. Even in the corner with all the outside liberties filled. I thought I'd solved it, but I hadn't, and it wasn't until I lost one in a game that I realized the gap in my knowledge. I think the self-doubt and book-doubt that engendered in me was worth two stones in strength instantly. Actually, maybe this is evidence not to look.
Malweth: I'm thinking of trying not looking at solutions - especially when using a computer interface (goproblems, palm pilot, etc). I find that "guessing" an answer using intuition is a very bad habit. It doesn't help at all with reading, though it does build intuition.
Spingle / Mr Tortoise (7k): Dont most go players lose > 50% of their games? (wouldnt this figure merley be a reflection of hte average relative strength difference?) Also with regard to tsumego, i think the object of the exercise as depicted above is not simply to get to the 'correct move', but to practise the process of solving itself. The 'correct' answer is not the final move but the thought getting to it - besides a tsumego is not a whole board problem and so it could be said (in the customary pedantic style) that they are not go. As for the use of intuition to solve a problem, this was third on the list because one has already exhausted all the other possibilities. In order to move in cases where you cannot read you have to trust your intuition. This move is also not a guess as you have already exhausted your ability to read. Your 'guess' proceeds from this knoweldge. Hopefully this brings some problems and the author together.
Charles: shouldn't sufficient and necessary carry different meanings? Above you seem to use them in teh same way. Sufficient for you would seem to gurantee progress ... this would seem to conflate this with necessity. Surley no necessary progress follows from the conditions which when satisfied are sufficient for progress to take place.
Malweth: I believe a final answer for a tsumego is found when you are 100% positive that you have the correct answer. This is one of the reasons many people think the answer should always remain hidden (zen koan-like). In terms of reading in a game, there are two issues at stake: the difficulty of the problem to be read, and the time available in which to read it. As a go player we strive to push our reading ability toward a correct answer (100% certain of the result), but as a time constrained player, this is not always possible. I believe this is the reason there are three levels of tsumego difficulty: easy (within 1-30 second problems), average (within 30-60 second problems), and difficult (within 1-5 minute problems). These also correspond to the desire we have in games to: 1) quickly find vital points and 2) quickly read out possibilities for each vital point, leading to a (hopefully correct) solution to a problem.
RBerenguel: I've read this page, and others similar a few times, and what kept me from doing what you (and others) suggest was tsumego. I hated it, don't know why. When I was playing, fine. No problem, I'll connect, kill, try to live, whatever. But pure tsumego, that I hated. Well, I started again with go, and with Kageyama's wonderful ladder, and with Graded Go Problems for Beginners (vol3, I think). And started to love tsumego, after six or seven days of doing problems at the train or bus. These days I'm just going through GoProblems, today I did (in short bursts) 74 problems. And enjoyed it a lot, something that a month ago wouldn't have happened. Want to improve, so let's do also the other ones. And thanks for this page, and sharing your thoughts while in Japan and Korea.
OhkenDruid?: Based on the comments on GoProblems, it is quite common for people to believe they have solved a problem, but for others to show them a refutation of their idea. In many cases it's the person that posed the problem that made the mistake. I therefore don't think people that are 100% positive about their solution have, in fact, always found correct solutions. This does not imply that a Go student should necessarily look at solutions, but it means that a commonly stated reason for not looking at solutions is incorrect.
Dieter: I want to continue a bit on the necessary/sufficient line by Charles and I have a new question for Ben too. Nowadays I tend to ask questions to those I teach (there is no better player to teach, unfortunately) rather than give answers, and I emphasize reading. I do not agree with Charles that improving your reading is necessary: I think there are ways to improve without improving reading. But improve your reading and you'll improve your game. So, it really is a sufficient condition for improvement, but it is not sufficient for becoming exceptionally good (it is necessary I think).
What interests me more is the meta-question of human learning: the tsumego/reading approach seems to put faith in man's reasoning. The replay pro games approach seems to put more faith in man's capacity to imitate. Nowadays we're told that imitation is wrong and reasoning is good. A very Western idea, which seems to be succesful when applied by the Koreans to Baduk. Could it be that the Japanese still favour a culture of imitation but that they meet the boundaries of success by imitation? Have we, at all, exhausted the power of imitation, which has been so succesful since primitive ages, as a society?
Benjamin (2008-11-19): Huh, this is getting very philosophical... Let me just answer about the Japanese Go, for the rest I have to think first =). Many Japanese amateurs definitely have the problem of always imitating what the teachers say without mush reasoning on their own. But the pros know better, so I don't believe imitation is a cause for the bad international performance of Japanese pros.
Imagist: *Testimonial tone* For months I had been keeping a 2:1 win:loss ratio on KGS, so needless to say my rank had been improving rapidly; about two stones per month (not counting the stones improvement when the KGS ranking system changed recently). Then at about 5 kyu I hit a block and couldn't seem to improve. For about 3 months I hovered in the upper levels of 5k, unable to improve. Then I started using Benjamin's method of studying tsumego, and the improvement was almost instantaneous. Of course, there was a week-long period where I couldn't seem to stop trying to kill everything and my win:loss ratio dropped to 1:3. But soon I was able to control my kill instincts and I'm now happily 4k. */Testimonial tone*
That said, here is a good place to get problems without the solutions (printable for those who prefer treeware like myself): tasuki's tsumego collections.
Malcolm (2008-01-11) I do not agree with this tsumego study method of not looking at the solution. I think looking at the solution can often be beneficial. Just my opinion. Personally I like trying problems a little too hard for me, and thinking them over for some time. For problems I can't solve, I find it useful to see the proposed solution. It's often a source of new ideas. At the moment this applies to my intermittent study of Xuanxuan Qijing problems, before that to work with train like a pro. It's beneficial to look at a solution when one has first done enough preliminary thinking on the problem. Also it helps to think about the given solution - one shouldn't just accept it blindly. This way once in a while you may find errata in books, you have to be willing to think for yourself.
Benjamin (2008-11-19): It is right looking at a solution after reading on a too hard problem won't hurt your go - instead, it might really help you getting new ideas. But it takes away the chance of really solving it on your own later, as you don't need to go through the hard process of getting closer to the solution step by step. If you have a huge collection of problems or a very bad memory, this is not a problem - but if this is one of the four tsumego books you own, you lost say half of the training effect of this one problem.
Malcolm (2008-12-03): Kobayashi Chizu-sensei also discusses this issue, as reported in godiscussions. I just came across the link. Personally, I'm not sure the training effect of having found the solution yourself is so important for all. Maybe it depends on the person? One can't re-invent the wheel for everything.
Mike?: This was the same conclusion I've reached. I've only played overall a couple of months. I quit during summer and came back during the fall with an even better understanding of the game somehow. I'm currently studying the "Master" games by Go-Seigen and Shusaku and it's my belief that replaying those games from memory could help you reading ability since you can memorize where all those stones are placed. Studying problems is a great way to learn about which shapes live/die, but I've discovered that life/death aren't so quick to arise in games where someone isn't completely engulfed with the idea of capturing a corner.
Coldnight You are mistaken I believe. Replaying and memorizing games might help you remember where moves are played but that is not what reading is about. Reading is more about learning and understanding shapes,memory has very little to do with it. The main reason you don't see those shape in you're games as often is that the shapes and tesuji that exist are there, but they are not as simple as they are in the problem itself. You might not see this yet but reading in a higher level is not about trying every move you can . Reading is about finding the idea or defect of the shape and using it with as little reading as you can, and life and death problems teach you how to do exactly that.
Phelan: "Reading is about (...) using it with as little reading as you can(...)." This is contradictory. You are talking about the shortcuts in reading, not reading itself. The shortcuts reduce the width and depth you need to read, but you still have to read. And for that, you do need memory.
Coldnight:I will try to explain this better : I did not mean you do not need memory but that it is a very little part of what reading in go is about: and yes "Reading (in go) is about (...) using it with as little reading (simply reading ahead) as you can(...)."
I was talking about the concept of reading in a go game in contrary to simply reading out every variation. Those are two different ideas,you see we do not try to read every thing out all the way while playing go, we try to understand the ideas of the moves and the aji there is in the shape.
Phelan I understood what you are saying, and I agree that reading everything out all the way is pointless, since no human (or computer, for that matter) can do that yet. However, to me, reading is the methodical analysis of lines of play, both in depth(how many moves in a line), and in width(how many alternatives at one move). This is the "meat" of reading. It's not just me saying it, Kageyama says so in LessonsInTheFundamentalsOfGo(I probably got it from there). Understanding the ideas of the moves, and the aji in a shape is a shortcut, in the sense that you don't need to read some alternatives (reduces width), and that you don't need to read some lines as far(reduces depth). When you get stronger, you actually need to read less. So to me, reading is not what you say it is. Do you understand what I mean, or must we agree to disagree? :)
Tesu-Jim: As every kyu player I want to be a 5-dan badly. Here I just wanted to talk about a little thing that I think is not mentioned anywhere (I might be wrong, couldn't yet read everything on SL...): when I do a tsumego-problem which is too hard for me (maybe not by much, but still), there's a tendency to feel _ashamed_ (!!) if I cannot solve it. I guess it stems from this very strong wish to already be a 5-dan and from the discrepancy with my actual rank (which, as of Oct 21st 2013, is that of a lowly German 7-kyu). The embarrassment is strong, even though I'm alone in the room, no dan-player around and no reason to feel ANYTHING. Feelings shouldn't enter the equation. But they do. So here's my advice for problem solving: _FEELINGS SHOULD NOT ENTER IT_. It strikes me as a good idea to remind myself of this from time to time. I know it seems a little obvious, and most every Go-player sees herself as this totally rational computerlike always-the-best-move reading-monster, but being human we all are creatures of emotion. (Even the best of the best sometimes play impulsively.) Just because one wants to be much stronger quickly there is no reason to feel inadequate when not solving problems correctly right away or when solving them too slowly. This feeling is totally uncalled for, and, above all, it's very distracting/unhelpful.
Also: when I cannot solve a problem, I sometimes console myself by thinking "Well that exact problem is not for me then" or, even worse, "that's a problem for much later" when I _know_ that I should persevere NOW. Certainly _some_ problems really _are_ for later, but many just aren't.
What I want to add to the tsumego-discussion is this: I think that looking at the solution _after_ you've really spend a LONG time trying to do a certain tsumego is not as a rule the wrong thing to do. By trying in isolation and totally by oneself to really solve _everything_ that there ever has been one would spend an inordinate amount of time. Generally speaking, spending lotsa time with the game is, of course, the one and only way to make progress. But IMHO there is no reason _not_ to learn some _other_ things about go (moves or shapes or whatnot) because one fills most of the available time just with tsumego after tsumego after tsumego.
So _sometimes_ looking up a solution or sneaking a look at the first move or at the general idea, apart from being a very human thing to do, is probably best. By having tried very hard to solve a certain tsumego the brain has been primed and will take in the solution much better than by just looking it up right away. (This last bit about how the brain learns is not my invention or my original insight; I think it is common knowledge for people who specialize in examining the functions of the brain; probably many readers here have already heard about that mechanism.) Would it (the brain) take the solution in _even better_ by finding it by itself? Probably yes. But maybe not. And by spending too much time on _one_ problem (and what exactly "too much" means is everybody's guess and certainly depends on the problem at hand) one also foregoes the chance to do more _other_ problems.
To paraphrase: one doesn't learn anything about throw-in-tesujis by doing five hundred fifty-five very hard problems with eyestealing-tesujis appearing around the 13th move.
(All of the above is just one fellers opinion. It might change upon reaching 5-dan level...)
Luis Sousa(kgs santiago1 4kyu) at the 2013 british go congress, I heard two little gems of wisdom from Michael Redmond, first he told me to do as many easy problems I could find and second(unrelated), was about direction of play, he said moves should not be made near strong groups. I suppose it reverts back to the simple check list of Do I have weak groups? Does my opponent have weak groups? Where are the big moves?.
See also: Teach Yourself Go