Banquets of the Black Widowers — Isaac Asimov

Six distinguished gentlemen (Ph.D.'s all) and one invited guest dine monthly at New York's elegant Milano restaurant. The Black Widowers, whose number includes the peerless waiter, Henry, have an uncanny ability to elicit from each guest a story that is somehow problematic, unsolved, a mystery--even if the guest is unaware of the problem.

But the Black Widowers, equipped with plenty of erudition and intuition, eagerly tackle the puzzle--until Henry, quietly amassing the facts, delights them all with the answer.