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Slightly different approach than much of what has already been posted.
1) Assume that the list is sorted
2) Note that when we do our sum, digits in the same position can exist in either number and provide the same result: eg, 145 + 39 vs 135 + 49. This solution provides only the sum, not the list of possible ways to get there.
3) backtrack through the numbers to put digits in their right spots right away
- superEGO December 05, 2013