In Tucson there is a hundred-room hotel—ten floors, ten rooms per floor—that has been empty and boarded up for years. It’s located near my father’s office downtown, and every evening, when he calls to tell me he won’t be home for dinner, I know that he is going to meet his mistress at the hotel. I devise a plan to catch him out. Every night I will also go to the hotel and, since I don’t know where the meeting will take place, I will choose rooms in random series. I can visit three rooms per night, spending two to three hours in each. Sometimes I go in sequence down one hall, sometimes I take the elevator up and down several stories. I know it will be a long time before I chance on my father, but I am determined in my plan until one night he does come home and, in a fit of tenderness, confesses what he’s been up to and, furthermore, that he and his mistress have been playing the very same game that I have, visiting three rooms per night in random series, without having yet found each other. My head spins with combinatorics: if all three of us are moving independently through the hotel, how long can we go before the odds compel that two of us meet? Will my father find his mistress, or will I surprise my father? Or will I meet the mistress without my father present? And what would happen then?
