Date: Wed, 25 Aug 1999 18:40:03 EDT
Dear Math Central:
Here's the question:
You have three containers. Container 1 is a three (3) liter container. Container 2 is a five (5) liter container. Container 3 is an eight (8) liter container that is full of liquid. The goal is to get 4 liters in one of the containers.
Stipulations: There are no marks on the containers to measure out the liquid.
All you know is that 1 is 3 l., 2 is 5 l., and 3 is 8 l. full of liquid.
I started out with a chart like this
A great reference for this problem is
H.S.M. Coxeter and S.L. Greitzer, Geometry Revisited, Random House, 1967.
The authors use geometry, in particular reflections, to study this and similar problems. They include a solution to your particular problem that involves only 6 pours. Using your notation the solution is:
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