Well, first of all, the fact that a go puzzle might have more than one variation isn't a "problem"... solving the problem requires distinguishing between (i) best play for both sides, (ii) "stubborn resistance", (iii) lines which are approximately equal, with perfect play depending on the rest of the board, and (iv) inferior lines.

But anyway, you seem to be looking exclusively at a very easy class of go problem, the sort aimed at complete beginners. Frequently you'll get a group of puzzles about "atari". The goal is to put some stones in atari. Does that mean that you should put every single stone you see in atari? Of course not. But for the sake of beginners, we have these puzzles, so that they get comfortable with the idea of atari. Likewise we have puzzles about capture, and snapback, and bamboo joints, and extending. This doesn't mean that capturing stones, or setting up snapback, or making a bamboo joint, is always the right move whenever it's possible. But you can't teach these simple moves with whole board problems.

I'm just trying to go through the complete batch of 6350 exercises included in the Dong-Dong grouping, ranging from
30k to 10k. They contain a wide range of patterns, but I think it can still be interesting to look at even the most simple problems which can turn out to be confusing if you try to establish why certain answers are to be considered correct, like the example of exercise 0294 (rated 30k). It's not a difficult exercise and the goal is obviously to capture the three stones, but it's a rather subtle question whether or not they can best be captured directly or indirectly. I understand that the exercise doesn't imply that it's always the best choice to capture stones as soon as you can if you have the opportunity. But in general I'm also interested in meta-discussions regarding how tsumego can be employed to teach basic aspects of go to children or beginners. In fact, I also consider myself somewhat of a beginner, as I'm only 17k at tygem and wbaduk. So I'm openminded and I'm willing to listen to anyone who is able to explain things clearly. I do however take a critical attitude and try to ask questions when things are not clear.

I guess the main point I'm trying to make is that you can only learn from exercises when you see how the answer makes sense. You can just try to memorize answers in the hope that eventually you'll get a hang of the underlying pattern and you no longer need to memorize the correct answers and you can simply see what the correct answer should be if you look at it long enough or take enough time to consider the most obvious possible continuations from the given situation.
But the exercises are not perfect, so they might give incomplete or incorrect answers, so whenever I encounter a tsumego and I fail to understand why the given answer is to be considered the correct answer, I try to find out if there is perhaps an error in the exercise or whether it's simply a pattern that is hard to understand which means the exercise is correct despite my inability to comprehend why it's correct.

Right, what I'm Trying to say is that one common format for beginner exercises (and iirc beloved by godchild, tho I can't see their problems anymore) is providing a model and asking the beginner to copy the model a few times. It's a useful way to drill in concepts, but not a horribly sophisticated approach to the game. At the point where you're caviling about 30k problems, it's time to move onto something more challenging.

If the 30k problem is so easy, how come even dan players can't answer confidently what the correct answer should be?
Seems to me that these problems can be quite a challenge occasionally, though the vast majority of 30k problems don't take much effort. I think comparing and contrasting related tsumego is about the most sophisticated approach to achieve a more rigorous understanding of the underlying patterns in go (far more useful than a game review for instance).
What fascinates me in go is exploring the boundary between things I understand and things I fail to understand and seeking to expand that boundary.
GoChild is very helpful in that respect, because it allows me to go through a batch of exercises, mark the ones that I find the most tricky and being able to shuffle those marked problems to focus my attention on those and thereby avoiding wasting my time with things I've already mastered.

Well, look... if you have fun doing this thing where you revel in unintentional features of "repeat-after-me" 30k-rated problems, I have no problem with that. Fun is fun. But I will answer your question because I am gullible.

The answer to a puzzle depends on what question the puzzle is asking. You can take the same basic phenomenon and turn it around to look at it from multiple aspects, and then use those aspects to ask completely different questions about the phenomenon. For example, you could look at an arrangement of stones and ask "What's the count, locally?" Or you could ask "How many ko threats does White have?", or "How many points is the next move in this area worth?" or "What's the status of these groups?" There's no particular reason to expect two puzzles which are created by looking at the same stones in two different ways to be equally difficult. Likewise, there's no reason to expect that stones which are set up to give one puzzle a single unique answer will also provide a single unique answer to any puzzle which you might choose to pose about them.

So if you take a 30k problem which is designed to have an answer to the puzzle "How do you capture stones in this game?" and instead ask "Which of these two captures is better," there's not necessarily a correct answer. If you take a 10k problem which is designed to have an answer to the puzzle "How can black kill the white group?" and instead ask "How can white use the aji of the dead group?", there's not necessarily a correct answer. If you want more subtle puzzles, you need to find problems that were designed to be more challenging. But if you're having fun finding subtleties in easier puzzles, that's awesome too.

But how can you try to teach beginners something if you're not even sure what you're asking them?
A beginner sees the puzzle, might notice there are two ways to capture and wonder which of the two is best or whether both are equally good.
If the puzzle only accepts one of the two ways to capture as a solution, the beginner might assume that
means one of the two ways to capture is better than the other. But this is an assumption and unless you actually see a clear reason why one of the two ways to capture is better, you are left wondering why sometimes a solution is accepted and sometimes a potential solution is rejected and whether or not this signifies something that merits attention or whether the creator of the tsumego simply overlooked the alternative method or erroneously picked the inferior solution as the answer.

So if the purpose of the exercise is simply to teach beginners about methods to capture, all methods to capture should be accepted. If the purpose of the exercise is to teach beginners to try and look for more optimal ways to do something as opposed to inferior ways to achieve the same goal, you'd expect that the beginner should at least be able to verify for himself what the optimal and what the inferior way is, so that he might learn to recognize
the optimal way in situations that also involve inferior ways.

I don't care about the level of tsumego. All I care about if I can understand them and if I can't if that might be because there could be an error in the tsumego. I solve tsumego for beginners as well as tsumego that are more difficult, but when I seek to master a batch of exercises it seems to make sense to start with the most simple ones and work my way up towards the more complicated ones.
I'm not going over exercises I understand over and over again because obviously that wouldn't help me improve and would just be a waste of time, but I have no problems going through a large collection of tsumego that includes tsumego that are extremely simple to spot and mark the ones that somehow mystify me. So I bring that up on this forum and lo and behold, for some of those tsumego even dan players can't really confidently say if there is an answer that is to be preferred because it's optimal or whether all potential answers are equally valid.

This is a further argument for problems with good solutions in a language the student understands. In that case, you can say "these both capture, but this one does..."

Or if you're not concerned about that, you should accept both answers. If necessary, nudge the student towards the other.

_________________
Occupy Babel!

Suppose we have a problem with two ways to capture -- a ladder or a net.

If we are trying to teach the concept of ladders, then the ladder solution is best

If we are trying to teach the concept of nets, then the net solution is best

This is just an over simplified example to illustrate why not all solutions to a problem should be presented -- putting aside the fact that my particular example may in fact just be a poorly designed problem. More complicated problems may have legitimate multiple solutions, but not all solutions aid in teaching the intended concept/skill.

I think we all know that "best" solutions to problems can be be different depending on if its just a localized problem, or a full board problem. So "best" is relative.