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Lê Quốc Trần Anh Coordinator

22/07/2018 at 03:27
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The digital sum of a number is the sum of its digits. How many positive three-digit integers have a digital sum of 5?


Mathcounts


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  • ...
    Mr. Bee moderators 23/07/2018 at 01:52

    We have: 5 = 1 + 0 + 4 = 1 + 1 + 3 = 1 + 2 + 2 = 2 + 0 + 3 = 5 + 0 + 0

    With 1, 0, 4, we can have 4 three-digit numbers including these 3 numbers

    (104, 140, 401, 410)

    With 1, 1, 3, we can have 3 three-digit numbers including these 3 numbers

    (113, 131, 311)

    With 1, 2, 2, we can have 3 three-digit numbers including these 3 numbers

    (122, 212, 221)

    With 2, 0, 3, we can have 4 three-digit numbers including these 3 numbers

    (203, 230, 302, 320)

    With 5, 0, 0, we can have 1 three-digit number including these 3 numbers

    (500)

    In total, we have 4 + 3 + 3 + 4 + 1 = 15 (numbers)

    Lê Quốc Trần Anh selected this answer.
  • ...
    Lê Anh Duy 22/07/2018 at 14:28

    We have: 5 = 1 + 0 + 4 = 1 + 1 + 3 = 1 + 2 + 2 = 2 + 0 + 3 = 5 + 0 + 0

    With 1, 0, 4, we can have 4 three-digit numbers including these 3 numbers

    With 1, 1, 3, we can have 6 three-digit numbers including these 3 numbers

    With 1, 2, 2, we can have 6 three-digit numbers including these 3 numbers

    With 2, 0, 3, we can have 4 three-digit numbers including these 3 numbers

    With 5, 0, 0, we can have 1 three-digit number including these 3 numbers

    In total, we have 4 + 6 + 6 + 4 + 1 = 21 (numbers)


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