The Most Malicious Ma\^{i}tre D'

TL;DR

This paper introduces an optimal strategy for the malicious maître d' problem, improving previous strategies and deriving a formula for the expected number of diners without napkins, thus advancing understanding of this seating puzzle.

Contribution

The paper presents a new optimal strategy called 'long trap setting' for the malicious maître d' problem, surpassing previous strategies in effectiveness.

Findings

The 'long trap setting' strategy is proven to be optimal.

A formula for the expected number of napkinless diners is derived.

The new strategy outperforms earlier approaches.

Abstract

The problem of the malicious ma\^{i}tre d' is introduced and solved by Peter Winkler in his book Mathematical Puzzles: A Connoisseur's Collection [1]. This problem is about a ma\^{i}tre d' seating diners around a table, trying to maximize the number of diners who don't get napkins. Along with this problem, Winkler introduces a variation called the adaptive ma\^{i}tre d' and presents a strategy. This problem was later investigated and a better strategy was discovered by Acton et al. [2]. We describe an even better strategy which we call ``long trap setting" and prove that it is optimal. We also derive a formula for the expected number of napkinless diners under our optimal strategy.