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A problem in combinatorics

  1. Jun 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Let A be a 100x100 matrix such that each number from the set {1,2,...,100} appears exactly 100 times. Prove that there exists a row or column with at least 10 different numbers.

    2. Relevant equations


    3. The attempt at a solution

    I suspect that I should use the pigeonhole principle, but I can't think of a way to do so.
     
  2. jcsd
  3. Jun 16, 2011 #2

    lanedance

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    so as a start could you look for a contradiction by assuming every row & column can have 9 or less distinct numbers
     
  4. Jun 17, 2011 #3
    Solved it, thanks :)
     
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