2016 AMC 10B Problem 6

Isaac added two three-digit positive integers. All six digits in these numbers are different. Isaac's sum is a three-digit number S. What is the smallest possible value for the sum of the digits of S?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.