Only one answer allowed: which one to accept?

What is the standard in the community for choosing which answer to accept? When there are multiple solution to the question.

I understand that there have been question that ask about this before. However, the issue here is not in term of quality, which is something you can compare between answers. Here the answers are incomparable because they are all interesting in their own way.

Though I guess I should state my case more specifically here. I got this question here. I just recently managed to solve it. Now the first answer point to a theorem that is a special case, and it might or might not be able to generalize to the solution. But still an useful answer, since I did not know about that theorem. The second answer hint at a commonly accepted way to solve this problem, but turn out to use something too advanced for my level, though it definitely works because I have seen the proof. The comments below the question point to a blog, which contains a third proof that I think is rather innovative and beautiful (now it is a comment so I can't accept it, but I could make an answer myself and credit it to the blogger and the commenter). Finally, all these methods are actually not accessible to me (I don't have any of the necessary theorem in all my maths class-I only know them from physics class), and I found a solution that is embarrassingly elementary, directly from the definition, and that is the solution I would put in my homework (and it is rather short). I have not put it into an answer yet, but I could.

So basically, what answer should I accept:

• Standard non-elementary solution.

• Special case with simpler proof.

• Innovative and interesting solution out of nowhere.

• Very elementary solution that is still short.

Also, I am considering a related feature request (kind of like allowing multiple accepted answer, but not that simple). Should I put it here or make a new question?

• Accept the one that you find most helpful, using whatever metric you use to judge this. It is your accept vote: hand it out as you wish. (I think I'm largely repeating Willie's answer from the other meta-thread.) – user642796 Dec 9 '13 at 8:59
• Thing is, I find them all useful, each in their own way. Most useful for submitting my homework would be my own answer, but that is probably not a good answer mathematically. If they all give the same solution, but one is more completed, then I can pick out the most useful one. But here they are equally useful, just different. – Gina Dec 9 '13 at 9:06
• Roll a die, flip a coin, ask your favorite person to pick a number in a current range, rand() or variants of it, obtain U-238 isotopes and measure their radioactive decay apply SHA512 to the results - twice - and then sum the hexadecimal digits repeatedly until you have a single digit and use it modulo the number of answers you received. – Asaf Karagila Dec 9 '13 at 9:14
• As you didn't post an answer to that question accepting your own answer isn't an option. But seriously, it really is up to you, and it is a decision you have to make. (Only be sure to upvote all answers that are helpful.) – user642796 Dec 9 '13 at 9:40
• Just add a comment to your question, something to the effect of "I am grateful for all the answers as they have been very helpful to me. I have upvoted them all, but I can only select one. I've chosen [person]'s answer because ..." – Joel Reyes Noche Dec 9 '13 at 9:59
• Just accept the one you like most. Note : "like", not useful nor even correct. It is your right to choose. If there are two answers you can't decide, flip a coin. If you are only a little bit uncomfortable with the outcome based on the coin, still follow the coin. If you are very uncomfortable, accept the other answer instead. – achille hui Dec 10 '13 at 19:54
• Is it just me or is Meta overused recently? Try to think for yourselves people... (I'm not trying to offend anyone with this comment but really...) – dreamer Dec 13 '13 at 13:37
• @901301 sounds like a meta question to me. Of course that probably goes against your point... – person27 Dec 15 '13 at 18:04