Each time the procedure is used, the maximum difference between 2 numbers on the new list stays the same. 1st time :{9, 28, 21} and max diff = 19 2nd time : {49, 30, 37} and max diff = 19 ... and so on $\therefore \boxed{19}$

$$(a, b, c) \longrightarrow (b+c, a+c, a+b)$$\begin{align*} |(b+c)-(a+c)| &= |a-b| \\ |(a+c)-(a+b)| &= |b-c| \\ |(a+b)-(b+c)| &= |c-a| \end{align*}$$\text{Max}(|b+c)-(a+c)|, |(a+c)-(a+b)|, |(a+b)-(b+c)|) = \text{Max}(|a-b|, |b-c|, |c-a|)$$Thus, the maximum difference between two numbers in the list remains the same. $$\text{Max}(|20-1|, |1-8|, |8-20|)=\boxed{19}$$