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Math Help - Given any 12 natural numbers...

  1. #1
    Member billym's Avatar
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    Given any 12 natural numbers...

    Show that, given any 12 natural numbers, we can choose two of them such that their difference is divisible by 11.
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    Member billym's Avatar
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    nevermind i got it. didnt read the question properly (again)
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    Quote Originally Posted by billym View Post
    Show that, given any 12 natural numbers, we can choose two of them such that their difference is divisible by 11.
    If two number have the same remainder when divided be eleven then there difference is divisible by eleven. There are only eleven possible remainders, \{0,1,2,\cdots,9,10\}, when an integer is divided by eleven.
    You have twelve integers. What does that tell you?
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