The Monte-Carlo method applied to the Shabbat Elevator Event problem

Peter Stewart Cumber

doi:10.1080/0020739x.2025.2574950

The Monte-Carlo method applied to the Shabbat Elevator Event problem

Peter Stewart Cumber

School of Engineering & Physical Sciences

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Abstract

The Shabbat Elevator Event problem is the probability that people in a conventional elevator on the ground floor exit the elevator as it moves up the building, such that the elevator stops on all floors. This mathematical problem can be framed as a problem in combinatorics. In this paper, the Monte-Carlo method is applied to the Shabbat Elevator Event problem. This is a straightforward implementation of the Monte-Carlo method and is considered an ideal test problem for an undergraduate engineering student to use as a stepping stone to the application of the Monte-Carlo method to more advanced engineering applications. The Monte-Carlo simulations are compared with the analytical solution. The numerical performance of the Monte-Carlo method is analysed. The probability density function of the probability distribution for the Monte-Carlo simulations is shown to tend to the standard Normal distribution. 95% Confidence intervals for the predicted Shabbat Event probability are calculated. The Monte-Carlo method is also used to calculate the Shabbat ratio. The Shabbat ratio is the ratio of the probability of a Shabbat Elevator Event for P people and F floors compared to the probability of a Shabbat Elevator Event for (P + 1) people and (F + 1) floors.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	International Journal of Mathematical Education in Science and Technology
Early online date	13 Nov 2025
DOIs	https://doi.org/10.1080/0020739x.2025.2574950
Publication status	E-pub ahead of print - 13 Nov 2025

Keywords

Monte-Carlo methods
Shabbat elevator event
combinatorics
central limit theorem

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10.1080/0020739x.2025.2574950Licence: CC BY-NC-ND

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© 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License(http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
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abstract = "The Shabbat Elevator Event problem is the probability that people in a conventional elevator on the ground floor exit the elevator as it moves up the building, such that the elevator stops on all floors. This mathematical problem can be framed as a problem in combinatorics. In this paper, the Monte-Carlo method is applied to the Shabbat Elevator Event problem. This is a straightforward implementation of the Monte-Carlo method and is considered an ideal test problem for an undergraduate engineering student to use as a stepping stone to the application of the Monte-Carlo method to more advanced engineering applications. The Monte-Carlo simulations are compared with the analytical solution. The numerical performance of the Monte-Carlo method is analysed. The probability density function of the probability distribution for the Monte-Carlo simulations is shown to tend to the standard Normal distribution. 95\% Confidence intervals for the predicted Shabbat Event probability are calculated. The Monte-Carlo method is also used to calculate the Shabbat ratio. The Shabbat ratio is the ratio of the probability of a Shabbat Elevator Event for P people and F floors compared to the probability of a Shabbat Elevator Event for (P + 1) people and (F + 1) floors.",

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The Monte-Carlo method applied to the Shabbat Elevator Event problem

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