It is up to the OP to accept the answer which, in his eyes, is the best answer to a question. sometimes (in the case of your tagged question) it might not be as clear as to what the OP is thinking.
Though it stands to reason if there are multiple answers which are correct then the question is probably too broad, then again if there is a lateral thinking tag (not the case for your tagged question) I would say there will always be multiple possible answers. In case of the lateral thinking tag it is up to the OP to select the answer which best fits but also has some quality. Quality of an answer is relative though. You might say a well explained question like yours has more quality than the accepted answer. In other cases a very long answer, or one with many formula's proving a given answer might sometimes be less desirable, since it will be harder to understand for most. There an answer with a worded explanation which is shorter and well formulated might be the best answer to accept.
In questions without the lateral-thinking tag I would like to argue there should only be 1 possibility. If there are multiple like this question you need to refine your question by posting hints and expanding the question with more information to narrow the results (as the OP did) though posting hints and expanding a riddle is not a nice way to handle this, it is the best way i can think of.
Then after refining, if the question is still to broad it should be closed (if the OP can't add any more information without giving the answer away).
In the end it comes down to the OP (and the community).
The accept answer to a question with this tag should be either of the following:
- The one the community voted highest.
- The answer the OP had in mind.
- The answer which changed the OP's mind about being the best fitted as answer, which could be for comical or ecstatic reasons.
- if the question is too broad but can be refined to yield 1 true output it should be done by OP.
- if the question is too broad but can't be refined to yield 1 true output it should be closed as such.
Typing this I came to the realization, if the question is very well received by the community like the one mentioned it means the community does not view it as too broad and accept the possibility of multiple answers, in this case making a community post and accepting multiple answer might even be the best idea (?)