# Fetching Water with Least Residues

In a classic pouring problem, given two 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.

Author(s):
Herb Bailey
Publication Date:
Monday, June 9, 2014
Original Publication Source:
College Mathematics Journal
Original Publication Date:
September, 2008
Subject(s):
Algebra and Number Theory
Number Theory
Diophantine Equations
Topic(s):
Number Theory
Diophantine Problems
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Applicable Course(s):
4.3 Number Theory
Modify Date:
Monday, June 9, 2014