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Measuring with Two Jugs

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a
5
b
7
c
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x+y0
d
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This Demonstration shows a graphic solution of the problem of measuring out
c
liters of a liquid using jugs of capacity
a
and
b
liters, with
a,b,c
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
ax+by=c
with minimal
|x|+|y|
. Another method for solving the equation
ax+by=c
can use two rulers with lengths that are multiples of
a
and
b
. The problem cannot be solved if
gcd(a,b)
does not divide
c
.
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