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Sam Loyd's Courier Problem with Diophantus, Pythagoras, and Martin Gardner

by Owen O'Shea

This article originally appeared in:
College Mathematics Journal
November, 2008

Subject classification(s): Algebra and Number Theory | Algebra | Equations | Number Theory | Famous Problems
Applicable Course(s): 4.2 Mod Algebra I & II | 4.3 Number Theory

In Sam Loyd's classical Courier Problem, a courier goes around an army while both travel at constant speeds. If the army travels its length during the time the courier makes his trip, how far does the courier ride? In both revisions of this problem, a single-file army and a square army, the solution is irrational. Here, variations are considered in which the solutions are rational.   In fact, certain Pythagorean tripes can be used to generate problems that have integer solutions.

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Capsule Course Topic(s):
Number Theory | Diophantine Problems, Pythagorean Triples
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