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Math Help - Positive Integers

  1. #1
    Junior Member Dragon's Avatar
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    Positive Integers

    12 positive integers are written in a row. The fourth number is 4, and the 12 number is 12. The sum of any three neighboring numbers is 333.Determine the twelve integers
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Dragon View Post
    12 positive integers are written in a row. The fourth number is 4, and the 12 number is 12. The sum of any three neighboring numbers is 333.Determine the twelve integers
    You have the numbers: A,B,C,4,D,E,F,G,H,I,J,12

    You know that: 4+C+D=333

    Solve to get: C=329-D

    You also know that: 4+D+E=333

    Solve to get: E=329-D

    Therefore: C=E

    Using the same method you get that: B=D

    So you know that: C+4+D=333

    Substitute: C+4+B=333

    Solve: 4=333-B-C

    Note that: A+B+C=333

    Solve: A=333-B-C

    Therefore: A=4

    Using the same methods above you'll find that:

    A=4=F=I

    B=D=G=J

    C=E=H=12


    Remember that: D=333-4-C

    Substitute: D=333-4-12

    Then: D=317

    So the pattern is: 4,317,12,4,317,12,4,317,12,4,317,12
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