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2003 AMC 10B Problem 13

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2003 AMC 10B Problem 13AMC 10 Step by Step
Name:                             Date: September 13, 2026
Bases & Digits · difficulty 2 of 5 · about 3 min · position P11-15

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 ?

  1. A)

    33

  2. B)

    44

  3. C)

    66

  4. D)

    99

  5. E)

    1010

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