Conway's Napkin Problem

The Malicious Maitre D’ At a mathematics conference banquet, 48 male mathematicians, none of them knowledgeable about table etiquette, find themselves assigned to a big circular table. On the table, between each pair of settings, is a coffee cup containing a cloth napkin. As each person is seated (by the maitre d’), he takes a napkin from his left or right; if both napkins are present, he chooses randomly (but the maitre d’ doesn’t get to see which one he chose). In what order should the seats be filled to maximize the expected number of mathematicians who don’t get napkins? . . . This problem can be traced to a particular event. Princeton mathematician John H. Conway came to Bell Labs on March 30, 2001 to give a “General Research Colloquium.” At lunchtime, [Winkler] found himself sitting between Conway and computer scientist Rob Pike (now of Google), and the napkins and coffee cups were as described in the puzzle. Conway asked how many diners would be without napkins if they were seated in random order, and Pike said: “Here’s an easier question— what’s the worst order?”