The secretary problem:
A company is looking for a secretary.
n people apply, they are interviewed one after the other.
One can compare anyone only with the previously seen applicants.
Whoever is not chosen direcftly after the interview, is rejected for ever.
(odds-strategy, stop-index-strategy, Bruss-strategy):
Wait for a while, say until after interview number s (the "stop index").
Then choose the first one who is better then all the previous ones
(or else the last one).
What is optimal?
Optimal is s = 1/e ≈ 37 %.
For the proof, one has to look also here at all permutations of n.