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Math Help - New question

  1. #1
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    New question

    Could you please answer for this

    show that in any group of 36 people, we can always find 6 people who were born on the same day of week.
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  2. #2
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    Re: Pigeon Hole Principle

    @suhail
    Try to prove that statement wrong: try to show that you can have 36 people, 6 of whom don't have to be born the same day of the week.

    How would this work? Well, we need LESS THAN 6 people to be born every day of the week.

    So: Monday: at most 5 people
    Tuesday: at most 5
    ...
    Sunday: at most 5.

    But notice, there are 7 days in a week and at most 5 people per day, which is 35.

    35 < 36 and we know if we increased any one of those days by 1, we'd be at 6 which we don't want!

    It follows that there are always 6 people born the same day of the week in a group of 36.
    Last edited by Plato; April 17th 2014 at 04:44 PM. Reason: This was a hijacked post
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  3. #3
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    Re: New question

    Hello, suhail!

    Show that in any group of 36 people, we can always find
    6 people who were born on the same day of week.

    Suppose you randomly ask people on the street their day of birth.
    . . And you want to find 6 people who have the same day.
    How many people must you ask?


    You could be very lucky.
    . . The first 6 people could be born on, say, Tuesday.
    So you could ask a minimum of 6 people.


    What is the very worst that can happen?

    You ask a large group of people and:
    . . 5 were born on Sunday,
    . . 5 were born on Monday,
    . . 5 were born on Tuesday,
    . . 5 were born on Wednesday,
    . . 5 were born on Thursday,
    . . 5 were born on Friday,
    . . 5 were born on Saturday.

    You have asked 35 people, and you still
    . . won't have 6 people on the same day.

    But the next person will have one of those days.
    Then you will have 6 people with the same day of birth.

    Therefore, you could ask a maximum of 36 people.
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