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Homework Help: Proof about

  1. May 2, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove that if one chooses more than n numbers from the set {1,2,3, . . . ,2n}, then one number is a multiple of another. Can this be avoided with exactly n numbers?
    3. The attempt at a solution
    If we pick the top half of the set n+1 up to 2n we will have n numbers that are not multiples of each other. the smallest multiple of n+1 is 2(n+1) but this is outside the set. and there are n numbers from n+1 to 2n. if i pick numbers below n+1 then their double would be in the top half of the set. so the best way to pick them is the top half of the set from n+1 to 2n
  2. jcsd
  3. May 3, 2014 #2


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    That certainly is a way to pick n without picking one that divides another. What about the proof that you cannot pick n+1?
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