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Fetching Water with Least Residues

by Herb Bailey

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

Subject classification(s): Algebra and Number Theory | Number Theory | Diophantine Equations
Applicable Course(s): 4.3 Number Theory

In a classic pouring problem, given two unmarked jugs with capacities \(m\) and \(n\) pints, where \(m\) and \(n\) are relatively prime integers, and an unlimited supply of water, the goal is to obtain exactly \( p\) pints, where \( p\) is an integer, \( 0 < p < m+n \). This capsule uses properties of least residues to show that there are two distinct pouring sequences to achieve the desired result. The more efficient sequence can be determined by solving a linear congruence.

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