1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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


    User Avatar
    Homework Helper

    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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook