Puzzle—A Mathematical Programming Approach for Mongolia’s “The Four Strongest” Puzzle

We describe a mathematical programming approach to solve a recently proposed puzzle from Mongolia. This puzzle involves physically laying out toys of four legendary Mongolian animals in different orientations and positions within a box such that they fit. The author of the puzzle finds a solution by...

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Bibliographic Details
Published inTransactions on education Vol. 25; no. 3; pp. 265 - 269
Main Author Singh, Bismark
Format Journal Article
LanguageEnglish
Published INFORMS 01.05.2025
Subjects
inclusion-exclusion principle
incomplete data
linear arrangements
mathematical programming
puzzles
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Summary:We describe a mathematical programming approach to solve a recently proposed puzzle from Mongolia. This puzzle involves physically laying out toys of four legendary Mongolian animals in different orientations and positions within a box such that they fit. The author of the puzzle finds a solution by an exhaustive enumeration of the exponentially many possibilities and by employing a series of axiomatic assumptions. In the absence of the physical toys (and, thus, their true measurements), could we use operations research to help us? We present one such approach and several exercises that could be tasked in an introductory course on mathematical optimization. Classroom activities provide us a diverse set of solutions for some of these exercises. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ited.2024.0112 .
ISSN:1532-0545
1532-0545
DOI:10.1287/ited.2024.0112