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Math Help - Number Problem

  1. #1
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    Dec 2009
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    Number Problem

    Hii

    Set this number problem as a "fun" extension homework, just can't get my head round it. The only way i see of figuring it out is through trial and error, and i really don't have time for that.

    Anyway, here goes:

    "Below is a puzzle containing 4 different letters, which each represent a different number (positive, integer). The "?" can be substituted for any of the numbers to achieve the totals. The total is the sum of all numbers on that row. Submit the each of the numbers."

    K + S + ? + ? = 14

    ? + ? + P + N = 48

    K + P + ? + ? = 27

    N + ? + N + S = 20


    So far i have that:
    4<N<18
    S<12
    K<12
    P<25




    NB: If u know a way to solve it, but don't have time to actually work out the answers, could you hit me up with a method for solving it?

    Cheers
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  2. #2
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    Cheers for the help guys, appreciate it.
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  3. #3
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    Quote Originally Posted by smurfyboy88 View Post
    "Below is a puzzle containing 4 different letters, which each represent a different number (positive, integer). The "?" can be substituted for any of the numbers to achieve the totals. The total is the sum of all numbers on that row. Submit the each of the numbers."

    K + S + ? + ? = 14

    ? + ? + P + N = 48

    K + P + ? + ? = 27

    N + ? + N + S = 20


    So far i have that:
    4<N<18
    S<12
    K<12
    P<25

    Cheers
    n is 9 or smaller (according to the fourth equation)
    Your approach of defining the min/max value of the variables is probably the key.



    Question:
    Could you recheck the fourth equation?
    Is it correct?
    Since you indicated n<18; if n + n + something = 20 then n cannot be greater than 10.
    Last edited by aidan; December 7th 2009 at 08:19 AM. Reason: added question
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  4. #4
    Super Member
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    Quote Originally Posted by smurfyboy88 View Post
    Hii Set this number problem as a "fun" extension homework, just can't get my head round it. The only way i see of figuring it out is through trial and error, and i really don't have time for that.
    Anyway, here goes:
    "Below is a puzzle containing 4 different letters, which each represent a different number (positive, integer). The "?" can be substituted for any of the numbers to achieve the totals. The total is the sum of all numbers on that row. Submit the each of the numbers."

    K + S + ? + ? = 14 Eqn1
    ? + ? + P + N = 48 Eqn2
    K + P + ? + ? = 27 Eqn3
    N + ? + N + S = 20 Eqn4

    So far i have that:
    4<N<18
    S<12
    K<12
    P<25

    NB: If u know a way to solve it, but don't have time to actually work out the answers, could you hit me up with a method for solving it?
    Cheers
    The variables k,s,p,n are "different positive integers"

    After a few observations:

    0 \le s \le 14

    0 \le k \le 3

    24 \le p \le 27

    7 \le n \le 10

    NONE of the values for n {7,8,9,10} work with the other value to have four equations as given.

    Something (or several things) are not correct.
    No solution is possible with the given data.

    .
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