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Thread: looking for a formula

  1. #1
    Oct 2012

    looking for a formula

    hi guys

    i'm interested in math but not so well inclined..

    just looking for a formula to complete this question i've got in my head. trying to make my day easier and needing some assistance!

    i need to divide a certain number of things into groups.
    each group can be either 2 or 3 objects..
    total number of groups has to be divisible by 4

    is there a formula i can wrap up all this info in neatly? i'm looking to solve it myself of course.

    thanks a bunch =)
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  2. #2
    MHF Contributor
    Sep 2012

    Re: looking for a formula

    Hey starfsmenn.

    Xi = {2,3} so as a function you could say X(0) = 2, X(1) = 3 and f(x) = X(x) where x is either 0 or 1.

    Now you have S total things but the number of groups needs to be divisible by four.

    Let N be the number of groups: then N % 4 = 0 and the % is the modulus which gives the remainder of N/4 just like you learned in primary school and early high school.

    You also have S = Sum of X_i from i = 1 to N.

    Because there are many possible combinations for the actual groups, there is no one formula to get all the X_i's.

    You can however look at the different combinations of the different configurations of groups and eliminate the ones that don't have N be a multiple of 4.

    So in short you have

    N = number of groups
    S = Total number of things
    X_i = number of objects in group i where i is a whole number from 1 to N and
    S = Sum X_i i = 1 to N
    N % 4 = 0.
    X(a) = 2 if a = 0 or X(a) = 3 if a = 1 and a can only equal 0 or 1.
    Thanks from starfsmenn
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