I've been solving a lot of math contest inequality problems last few days and sometimes when I solve the problem I can easily ''see'' the idea behind it's creation (for an example, one clever substitution and you get something equivalent to some well-known inequality).
But sometimes, even after solving the problem, I don't have the faintest idea how someone could even conjecture it. Usually, I'm left with the feeling I took the long way to the solution, and that there should be a shorter, more elegant one.
I'm sure there are people on math.se who contribute to math competitions and I would really like to see their process behind creating an inequality problem (on some example contest problem). I hope this question isn't too soft.