# Fetching Water with Least Residues

by Herb Bailey

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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