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2007 AMC 10AProblem 25P21-25~8 minPrint
Bases & DigitsModular ArithmeticBound the quantity above/below or estimate to pin it downOrganized listing / direct enumeration

For each positive integer nn , let S(n)S(n) denote the sum of the digits of n.n. For how many values of nn is n+S(n)+S(S(n))=2007?n + S(n) + S(S(n)) = 2007?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2007 12A #22.