1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That certainly is a way to pick n without picking one that divides another. What about the proof that you cannot pick n+1?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proof about
  1. Proof about less than (Replies: 1)

Loading...