AMC 10 Step by Step
2003 AMC 10BProblem 13P11-15~3 minPrint

Let (x)\clubsuit(x) denote the sum of the digits of the positive integer xx . For example, (8)=8\clubsuit(8)=8 and (123)=1+2+3=6\clubsuit(123)=1+2+3=6 . For how many two-digit values of xx is ((x))=3\clubsuit(\clubsuit(x))=3 ?

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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 2003 12B #8.