If you start with three number, the “addition machine” produces three new ones by adding together each pair of two. For instance from the numbers {3, 4,6} the addition machine makes {10, 9, 7}. If you use the addition machine again these numbers become { 16, 17, 19}. We feed the three numbers { 20, 1, 3 } into the addition machine and let the machine calculate 2013 times. What is the biggest possible difference between two of the three resulting numbers ?