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In this paper we study a variant of the Malicious Maître d' problem. This problem, attributed to computer scientist Rob Pike in Peter Winkler's book Mathematical Puzzles: A Connoisseur's Collection, involves seating diners around a circular table with napkins placed between each pair of adjacent settings. The goal of the maître d' is to seat the diners in a way that maximizes the number of diners who arrive at the table to find the napkins on both the left and right of their place already taken by their neighbors. Previous work described a seating algorithm in which the maître d' expects to force about 18\% of the diners to be napkinless. In this paper, we show that if the maître d' learns each diner's preference for the right or left napkin before they are placed at the table, this expectation jumps to nearly $1/3$ (and converges to $1/3$ as the table size gets large). Moreover, our strategy is optimal for every sequence of diners' preferences.more » « lessFree, publicly-accessible full text available January 17, 2026
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Shirman, Blake; Volkening, Alexandria (, ArXivorg)When you think of fish, what comes to mind? Maybe you think of pet goldfish, movie characters like Dory or Nemo, or trout in a local river. One of the things that all of these fish have in common is patterns in their skin. Nemo sports black and white stripes in his orange skin, and trout have spots. Even goldfish have a pattern -- it's just plain gold (and kinda boring). Why do some fish have stripes, others have spots, and others have plain patterns? It turns out that this is a tricky question, so scientists need tools from several subjects to answer it. In this paper, we use biology, math, and computer coding to help figure out how fish get different skin patterns.more » « less
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