I heard this problem in a form like this (it's not exact wording):
There are N bachelors. Girl evaluates each of them one after another to find the best one. She can either chose a current bachelor as a final solution, or she can proceed with the next one. At which moment she should stop?
What's the name of this problem? (i.e. how to google it?) I'm also curious, if there is any approach to solve this problem when number of bachelors is infinite?