2006 AIME I Problem 6

Let \mathcal{S} be the set of real numbers that can be represented as repeating decimals of the form 0.\overline{abc} where a, b, c are distinct digits. Find the sum of the elements of \mathcal{S}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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