A set of three numbers has both a mean and median equal to 4. If the smallest number in the set is 1, what is the range of the set of numbers?
If the mean of three numbers is 4, then their sum is 12.  Since two of the numbers are 1 and 4, the third number is $12-(1+4)=7$.  The range, which is the difference between the smallest and largest numbers, is $7-1=\boxed{6}$.