You interview candidates one at a time and must decide immediately whether to hire each one; once you pass, you cannot go back. To maximize the probability of choosing the best candidate, how many of the first candidates should you interview without hiring before making a decision?
Strategy: Always pass on the first k candidates and use them only to set a "best so far" benchmark. Starting with candidate k+1, hire the first candidate who is better than everyone you have seen so far.
If k is too small, you may hire too early because you have too little information; if it is too large, you may have already passed the best candidate. Mathematically, the probability of choosing the best candidate is highest when k ≈ n/e (about 37%).