Three one-gallon buckets of red, blue, and yellow paint are each two-thirds full. Without the ability to measure, is it possible to equally mix all of the paint through a finite sequence of pours from one bucket to another?
If a solution exists, then the intermediate stages all consist of a full bucket, a two-thirds full bucket, and a one-third full bucket. Also, all pours, except for the first pour maybe the final pour, must be from a full bucket. This is because an empty bucket is never helpful.
Under these constraints, there are only two choices for any intermediate pour, so the problem is fairly restrictive in nature, but I'm having a hard time keeping track of all of the proportions.
Edit: Considering Ross's observation below, it seems if a solution exists, the final state must consist of two full buckets and one empty bucket.