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Differences of numbers

  1. Nov 18, 2007 #1
    1. The problem statement, all variables and given/known data
    http://math.stanford.edu/~vakil/putnam07/07putnam1.pdf
    I am working on number 6.

    Consider the the ordered pairs (1,12),(2,13),...,(89,100). There are 89 of them. These are the pigeon holes.

    There are 55 numbers between 1 to 100 and each of them flies to one or two pigeon holes. So split all of the pigeons not equal to 1 and 100 in half to get at least 108 pigeons. Then we have 108 pigeons flying to 89 holes. So there must be two numbers that differ by 11.

    What is wrong with my logic?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 18, 2007 #2
    Maybe there is something wrong with the problem instead...
     
  4. Nov 19, 2007 #3
    anyone?

    This problem is really bugging me!
     
  5. Nov 20, 2007 #4
    please--I am probably just making a stupid mistake and I want to fix it!
     
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