Due March 28

This problem can be solved by trial and error. We consider this to be a medium problem, worth 15 points (5 for each of the three parts below). Send answers and questions to mathstat@uoguelph.ca

Suppose we have two buckets and a cauldron. The buckets have a known volume but no graduations or measuring marks. If we are allowed to make the following moves:

  1. Fill a bucket from a faucet,
  2. Empty a bucket into the cauldron, and
  3. Pour one bucket into another until the first is empty or the second is full.
Then find the smallest number of moves to solve each of the following cases of the problem.
  1. Put 19 gallons in the cauldron with a 4 gallon bucket and a 9 gallon bucket.
  2. Put 16 gallons in the cauldron with a 3 gallon bucket and a 11 gallon bucket.
  3. Put 4 gallons in the cauldron with a 5 gallon bucket and a 7 gallon bucket.

Send your answer to mathstat@uoguelph.ca

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