Is there a way to differentiate answers that are googled verses derived? If so I would suggest you award the answer which provides the best explanation as to how the answer if found. I believe you should reward the best answer, not necessarily the people you feel put more work into their answer. Solving the problem alone, however, does not make it a good answer.
In my case (the only answerer at this time to the referenced question) I just remembered what the answer should look like having seen/answered the question before. If someone rigorously shows this is the only solution or shows how to find it, that would be a better answer. I personally don't feel that posting a well known problem like this is an appropriate use of this site and wanted to shut it down quickly. It is definitely different if the person has a question about the well known problem, has a variation on this problem, or reasonably expects (and states as such) that there are more answers than the traditional one. None of these apply to this question.