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Set- i do not understand the question

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the maximum size of a subset, P, of {1, 2, 3, . . . , 50}
    with the property that no pair of distinct elements of P
    has a sum divisible by 7?


    2. Relevant equations



    3. The attempt at a solution

    smallest sum = 3
    largest sum = 99

    factors of 7:

    7 14 21 28 35 42 49 56 63 70 77 84 91 98

    7 can be form by:

    1 6
    2 5
    3 4
     
    Last edited: Mar 16, 2009
  2. jcsd
  3. Mar 16, 2009 #2

    tiny-tim

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    Hi icystrike! :smile:
    ok … so if 1 is in P, what can't be in P? :wink:
     
  4. Mar 16, 2009 #3
    1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18 19 21 22 23 24 25 26 28 29 30 31 32 33 35 36 37 38 39 40 42 43 44 45 46 47 49 50 !!
    yes
     
    Last edited: Mar 16, 2009
  5. Mar 16, 2009 #4

    tiny-tim

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    no, that's what could be in P … what can't be in P are 6 13 20 27 34 41 48, in other words everything = -1 (mod 7)

    suppose 2 and 3 are also in P (as well as 1) … now what can't be in P? :smile:
     
  6. Mar 20, 2009 #5
    5 12 19 26 33 40 47
    4 11 18 25 32 39 46
     
  7. Mar 20, 2009 #6

    tiny-tim

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    ok, so if 1 2 and 3 are in, then all the mod6s 5s and 4s are out …

    can the other mod 1s 2s and 3s be in?
     
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