Thoughts on the Bucket Problem

An non-constructive solution to the "you have two buckets, 3 and 5 gallons, and must produce 4 gallons of water" problem:

  1. Fill the 3 gallon bucket.
  2. Empty the 3 gallon bucket into the 5 gallon bucket.
  3. Start pouring more water into the 5 gallon bucket.
  4. By the mean value theorem, the water will have reached 4 gallons at some point before it fills up.
changed June 10, 2009