This sounds like a special case of the secretary problem http://en.wikipedia.org/wiki/Secretary_problem http://en.wikipedia.org/wiki/Secretary_problem, where i

This sounds like a special case of the secretary problem http://en.wikipedia.org/wiki/Secretary_problem http://en.wikipedia.org/wiki/Secretary_problem, where instead of envelopes you swap secretaries and additionally you have a time constraint. I find it very interesting how these statistical problems can be projected on our own life (swapping jobs, finding a better partner etc ..)