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Old 2004-05-10, 14:11   #1
tom11784
 
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Aug 2003
Upstate NY, USA

2·163 Posts
Default buckets of water

The problem is that we have 3 buckets of water.

Bucket 1 has a capacity of 3 gallons and is initially empty.
Bucket 2 has a capacity of 5 gallons and is initially full of 50 degree water.
Bucket 3 has a capacity of 6 gallons and is initially full of 90 degree water.

Now the "non-real-life" conditions:

1) We can only move water between these three buckets.

2) We can purposely spill water, but once it's spilled we can't pick it back up. (so don't try this inside your home)

3) The water temperature will not change due to air temperature, change in pressure, etc.

4) When you mix water from buckets of different temperature, all the water becomes the average temperature before our next transfer. (no waiting for heat transfer - mixing 1 gallon of 50deg and 3 gallons of 90deg produces 4 gallons of 80deg)

5) We can only be precise when completely filling or emptying a bucket (i.e. pouring 3 gallons from the 6 gallon bucket into the empty 3 gallon bucket)

The puzzle is what integer temperatures between 50 and 90 can be produced?

This is not my puzzle, so I only have a partial answer.

HA! You thought this would be my partial answer, didn't you?

Also, this is the first puzzle I've posted so if anything seems unclear, let me know.
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