You are here

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.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

Capsule Course Topic(s):
Number Theory | Diophantine Problems
No votes yet