If I ask a question and get some answers for it of which all are equally correct and use a different method to solve the problem then how to decide which answer to approve?

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    $\begingroup$ Strictly your decision. No one can criticize it. Ok, if it turns out that the accepted answer is from your sister, or a classmate, then it will look like an inside deal, and we will criticize it. But this extra remark is meant to be parenthetical. No one else can tell which answer you find most helpful. $\endgroup$ – Jyrki Lahtonen Nov 18 '17 at 11:07
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    $\begingroup$ If some answerer tries to put some pressure on you, trying to make you select their answer in particular, that is not in the spirit of the site. Flag such comments for moderator attention, and we will deal with it. $\endgroup$ – Jyrki Lahtonen Nov 18 '17 at 11:09
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    $\begingroup$ It is up to you. IMHO, a reasonable decision procedure is: accept the one you "personally" find most useful. If equally useful, accept the one which has better quality. If same quality, accept the one which answered earlier. If answer arrived at around the same time, pick the one whose poster has lower reputation. If you still cannot decide, toss a coin. In those cases you "really" wish to accept more than one answer, thanks the other one in comment and point out you want to accept more than one answers. $\endgroup$ – achille hui Nov 18 '17 at 14:22
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Accepting an answer is the decision of the asker alone. Apply criteria that you find reasonable. It sometimes can make sense to communicate your decision in a comment. Also, you can still up-vote all answers you find useful. One sees comments of the following form with some frequency on non-accepted answers:

The alternative approach presented in this answer was very instructive to me, too. Because {some reason}. Unfortunately, I cannot accept more than one answer.

But don't overdo it either. Generally users know the system and thus understand that not all answers can be accepted. The non-accept itself should rarely be a problem. What may however be perceived negatively is an impression (possibly unjustified) of disregard for the answer if there is no noticeable reaction. In that sense I think it is reasonable to be quite generous with up-votes on answers to ones own questions.

Some criteria one could consider:

  1. Usefulness to you.
  2. Overall quality of the post (in your opinion).
  3. Effort expanded by the poster (in your perception).

If still in doubt, toss a coin maybe. Or, arguably the utility of the accept for a small account is rather higher than for a large account. Thus, chose the one with fewer points.

A non-criterion in my opinion is the time when an answer was given, especially if the difference is minor. To accept one answer over the other just because it was given thirty seconds earlier is in my opinion not a good practice, and might in a way even be detrimental to the quality of the site as it might encourage rushed answers.

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    $\begingroup$ I like your last paragraph. +1 We do need to discourage rushed answers (which might be sometimes half baked). $\endgroup$ – Paramanand Singh Nov 20 '17 at 16:13
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    $\begingroup$ @ParamanandSingh I have often seen users who do this : within the first minute of a question being put up, they quickly write a "punch line" i.e. something that encapsulates the answer. They then proceed to edit in steps, hoping that an early post would be noticed earlier, so getting more up votes. Also, if the answer is up voted, they sometimes even leave it incompelete, as is. Unfortunately, as mentioned in the last paragraph, these answers get accepted well before more informative answers can come up. I think this impatience should be discouraged, among new users. $\endgroup$ – Teresa Lisbon Nov 21 '17 at 10:36

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