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