The Most Malicious Ma\^itre D'
<|reference_start|>The Most Malicious Ma\^itre D': 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.<|reference_end|>
@article{madhavarapu2024the,
    title={The Most Malicious Ma\^{i}tre D'},
    author={Tejo V. Madhavarapu},
    journal={arXiv preprint arXiv:2407.09000},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09000},
    primaryClass={math.CO cs.DM}
}