Measuring with Two Jugs

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This Demonstration shows a graphic solution of the problem of measuring out liters of a liquid using jugs of capacity
and
liters, with
integers. The solution seeks the minimal number of times jugs are to be filled and emptied. So we are looking for a solution (in integers) of the Diophantine equation
with minimal
. Another method for solving the equation
can use two rulers with lengths that are multiples of
and
. The problem cannot be solved if
does not divide
.
Contributed by: Izidor Hafner (January 2016)
Code from: Emmanuel Garces Medina
Open content licensed under CC BY-NC-SA
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"Measuring with Two Jugs"
http://demonstrations.wolfram.com/MeasuringWithTwoJugs/
Wolfram Demonstrations Project
Published: January 7 2016