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math

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My sister is playing a dart game at an arcade. She can earn 2, 3, or 6 points with each dart. She scored 24 points. How many ways could she score 24 points given that each dart thrown landed on the dart board?

  • math - ,

    2 & 3 are both factors of 6.
    Meaning whenever 6 goes in a set, it can be replaced by two 3's or three 2's.

    6 * 4
    6 * 3; 3 * 2
    6 * 3; 2 * 3
    6 * 2; 3 * 4
    6 * 2; 2 * 6
    6 * 2; 3 * 2; 2 * 3
    6 * 1; 3 * 6
    6 * 1; 2 * 9
    6 * 1; 3 * 4; 2 * 3
    6 * 1; 3 * 2; 2 * 6
    6 * 0; 3 * 8
    6 * 0; 2 * 12
    6 * 0; 3 * 6; 2 * 3
    6 * 0; 3 * 4; 2 * 6
    6 * 0; 3 * 2; 2 * 9

    1 + 2 + 3 + 4 + 5 = 15 ways.

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