Interactive secretary problem: see candidates one at a time, decide to hire or pass. The optimal strategy observes the first 37% then takes the next who beats all seen. Converges to 1/e success probability.
The secretary problem: N candidates arrive in random order. You must accept or reject immediately (no recall). Optimal strategy: reject first r*=⌊N/e⌋ candidates, then accept first who beats all previous. P(success)→1/e≈0.368 as N→∞. Generalization: rank-based stopping (Cayley 1875, Lindley 1961). Cardinal version: Moser's problem — maximize expected value (not just rank). Connection: exploration-exploitation in multi-armed bandits.