The menage problem

• Main Authors: Sia, Sharon Marjorie D., Aquino, Jorjette B.
• Format: text
• Language: English
• Published: Animo Repository 1995
• Subjects: Permutations; Combinatorial analysis; Problem solving; Functions
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16266
• Institution: De La Salle University

This thesis presents two solutions to the menage problem, namely, Kaplansky's and Touchard's. The menage problem is an example of a derangement problem which uses the Principle of Inclusion-Exclusion, Addition Principle and Multiplication Principle. These two solutions made use of different conditions for the problem. Kaplansky made use of the tradition of seating the ladies first while Touchard made use of the idea of dominoes.The solution of Kaplansky was taken from Scripta Mathematics (1956) while Touchard's solution was taken from the article A Non-Sexist Solution to the Menage Problem by Bogart and Doyle. Definitions for functions and some principles like Addition, Multiplication and Bijection Principle are provided for better understanding of the solution. In addition, two equivalent formulations of the menage problem and one related problem are given.