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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
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