Authors : Sadia Ferdousi; Sujana Azmi Polin

Volume/Issue : Volume 9 - 2024, Issue 11 - November

Google Scholar : https://tinyurl.com/56xxsrk3

DOI : https://doi.org/10.5281/zenodo.14525005

Abstract : A puzzle is a problem or game that check an individual’s reasoning ability. The article explores some classical puzzles using mathematical concepts. The historical significance and the concepts of mathematics which have been applied to these puzzles have also been discussed. In this article, the famous Josephus’s problem, the Tower of Hanoi problem, the Cutting Pie problem and Travelling the World Problem, have been illustrated. The explanation of Josephus’s problem describes how elimination works in a circular sequence and how to maximize cuts from a circular region in the cutting-the- pie-problem. Recurrence relation is derived and the proof is established using mathematical induction. It also focuses on finding the shortest path on a dodecahedron in analyzing Travelling the World Problem which uses graph theory to find a Hamiltonian path. The existence of such a path is demonstrated. This article explores the real-life origins of these well-known problems and highlights their significance in understanding mathematical ideas. The detailed solutions to each puzzle will give readers perception into recursion, optimization, geometric properties, and the fascinating historical backgrounds of these puzzles.

Keywords : Puzzles, Josephus Problem, Tower of Hanoi Problem, Cutting Pie Problem, Travelling the World Problem, Hamiltonian Path.

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