A More Malicious Maitre d'

TL;DR

This paper analyzes a classic puzzle about seating diners to maximize napkin availability, evaluates Winkler's proposed solution using combinatorics, and introduces a new, more effective strategy.

Contribution

It provides a combinatorial analysis of Winkler's solution and proposes a novel strategy that outperforms previous methods.

Findings

Winkler's solution is not optimal based on combinatorial analysis.

The new strategy achieves a higher expected number of satisfied diners.

The paper advances understanding of optimal seating arrangements in this puzzle.

Abstract

In this paper we study the problem of the Malicious Maitre d', as described in Peter Winkler's book Mathematical Puzzles: A Connoisseur's Collection. This problem, attributed to computer scientist Rob Pike, involves seating diners around a circular table with napkins placed between each pair of adjacent settings. The goal of the maitre 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. Winkler proposes a solution to the problem that he claims is optimal. We analyze Winkler's solution using tools from enumerative combinatorics, then present a new strategy that performs better.