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Math Help - Problem

  1. #1
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    Problem

    (PEEM)base 5 + (PEEM)base 7 = (PEEM)base 8

    in this equation each of the letters represents a numer.
    Like e is 3 and m is 6 and p is 5.
    So what number does "Peem" represent?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Horror View Post
    (PEEM)base 5 + (PEEM)base 7 = (PEEM)base 8

    in this equation each of the letters represents a numer.
    Like e is 3 and m is 6 and p is 5.
    So what number does "Peem" represent?
    The setup is
    PEEM_5 = P \times 5^3 + E \times 5^2 + E \times 5^1 + M \times 5^0 = 125P + 30E + M

    PEEM_7 = P \times 7^3 + E \times 7^2 + E \times 7^1 + M \times 7^0 = 343P + 56E + M

    PEEM_8 = P \times 8^3 + E \times 8^2 + E \times 8^1 + M \times 8^0 = 512P + 72E + M

    So the problem reads:
    (125P + 30E + M) + (343P + 56E + M) = (512P + 72E + M)

    44P - 14E - M = 0

    Now, we know that P, E, and M are all less than 5 since PEEM is a number in base 5.

    So we can start by postulating P = 1:
    14E + M = 44

    M is at most 4, so we need E to be at least 3. (And, as it turns out, less than 4.) So try E = 3:
    M = 2.

    So PEEM = 1332 works.

    I can find no other solutions.

    -Dan
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  3. #3
    Senior Member TriKri's Avatar
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    Since E and M is < 4, 14 E + M is < 15*4 = 60. Any P > 2 would make 44 P > 88, hence the equation doesn't meet in both ends. So P < 1. P = 0 makes 14 E + M = 0, which only solution is E = M = P = 0.

    So PEEM is either 1332 as topsquark pointed out or 0000.
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