Puzzle - a mathematical programming approach for Mongolia’s “The Four Strongest” puzzle
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 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.
inclusion-exclusion principle, incomplete data, linear arrangements, mathematical programming, puzzles
265-269
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
May 2025
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
Singh, Bismark
(2025)
Puzzle - a mathematical programming approach for Mongolia’s “The Four Strongest” puzzle.
INFORMS Transactions on Education, 25 (3), .
(doi:10.1287/ited.2024.0112).
Abstract
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.
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singh-2024-a-mathematical-programming-approach-for-mongolia-s-the-four-strongest-puzzle
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Accepted/In Press date: 5 November 2024
e-pub ahead of print date: 29 November 2024
Published date: May 2025
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Publisher Copyright:
© 2024 The Author(s)
Keywords:
inclusion-exclusion principle, incomplete data, linear arrangements, mathematical programming, puzzles
Identifiers
Local EPrints ID: 496372
URI: http://eprints.soton.ac.uk/id/eprint/496372
ISSN: 1532-0545
PURE UUID: 1e2a8cc7-e2e3-4503-9423-10053b081e01
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Date deposited: 12 Dec 2024 18:03
Last modified: 03 Sep 2025 02:07
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Author:
Bismark Singh
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