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Math Help - Show that at least 3 of any 25 days chosen must fall in the same month of the year?

  1. #1
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    Show that at least 3 of any 25 days chosen must fall in the same month of the year?

    Show that at least 3 of any 25 days chosen must fall in the same month of the year?
    (I think I might have to use Proof by Contradiction, b/c we haven't done counting yet)

    I am not sure how to do this?. I am thinking this:

    There is 12 months in a year, and at least 3 means x > 3. So 3 * 12 = 36.

    But I dont think its right though.
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  2. #2
    Junior Member ursa's Avatar
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    Quote Originally Posted by Grillakis View Post
    Show that at least 3 of any 25 days chosen must fall in the same month of the year?
    (I think I might have to use Proof by Contradiction, b/c we haven't done counting yet)

    I am not sure how to do this?. I am thinking this:

    There is 12 months in a year, and at least 3 means x > 3. So 3 * 12 = 36.

    But I dont think its right though.
    hi
    here you have to choose 25 days
    there are 12 months in a year
    if we assume to take equal number of days from every month
    then it gives 2 days from each month
    and now 1 day is left to choose( b'cose 12*2=24 days we already chosen)
    we have to choose that one day out from one of the 12 month
    which ever be the month, there will be atleast one month from which 3 days will be chosen
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  3. #3
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    Quote Originally Posted by ursa View Post
    hi
    here you have to choose 25 days
    there are 12 months in a year
    if we assume to take equal number of days from every month
    then it gives 2 days from each month
    and now 1 day is left to choose( b'cose 12*2=24 days we already chosen)
    we have to choose that one day out from one of the 12 month
    which ever be the month, there will be atleast one month from which 3 days will be chosen
    I see now. Thanks for the help ursa.

    This is not my kind of math. I prefer Differential Equations than this..
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