A small question about mixing:
Consider the following 
The 5 gal bucket is full. What happens if we attempt to pour the contents of the 6 gal bucket into it? Obviously, we will spill 6 gal. But at what temperature? Do we assume that there is absolutely no mixing (The original 5 gal @ 50 degrees remains in the bucket and the 6 gal @ 90 degrees gets spilled) ?
or this 
Pour out 3 gal of 90 degree water. The remaining water has an average temperature of (5*50 + 3*90)/8 = 65 degrees. Unfortunately, none of the water is at that temperature. However, we can mix the water in the 3 buckets a (infinite) number of times and get it all to the same temperature.
Is the procedure allowed?
