What signs are there that a problem is solvable? [closed]

What signs are there that a problem is solvable, but not so easy that it isn't worthwhile doing, and not so hard like P=NP?

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These are not particularly easy questions, hence the need for an advisor for one's first attempts at doing mathematical research. – Cam McLeman Aug 17 2010 at 17:50
I am skeptical that there is a worthwhile general answer to this question. – Pete L. Clark Aug 17 2010 at 17:54
42  – Victor Protsak Aug 17 2010 at 17:57
Usually having a solution would be a sign that it is in fact solvable. – Asaf Karagila Aug 17 2010 at 18:14