Results 1 to 2 of 2

Math Help - Suppose that n+1 integers are chosen from the set {1 , 2, ..., 2n}.

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    2

    Suppose that n+1 integers are chosen from the set {1 , 2, ..., 2n}.

    Suppose that n+1 integers are chosen from the set {1 , 2, ..., 2n}. Show that at least
    one is even. [HINT: Think about how many odd numbers there are in this set]

    I was taking a look at this problem.... and think im doing it wrong because the answer seems too obvious.

    My reasoning is that for any n in N, one of the numbers will always be even, and prove this by

    n(0) n+1 = 1 = 1,2
    n(1) n+1 = 2 = 1,2,3
    n(2) n+1 = 3 = 1,2,3,4

    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Privoxy View Post
    Suppose that n+1 integers are chosen from the set {1 , 2, ..., 2n}. Show that at least
    one is even. [HINT: Think about how many odd numbers there are in this set]

    I was taking a look at this problem.... and think im doing it wrong because the answer seems too obvious.

    My reasoning is that for any n in N, one of the numbers will always be even, and prove this by

    n(0) n+1 = 1 = 1,2
    n(1) n+1 = 2 = 1,2,3
    n(2) n+1 = 3 = 1,2,3,4

    Cheers
    The set {1 , 2, ..., 2n} contains n even and n odd numbers. Pidgeonhole principle...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How many 7-card hands can be chosen
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 16th 2011, 01:54 PM
  2. Replies: 6
    Last Post: March 2nd 2011, 01:36 AM
  3. Why was this definition of variance chosen?
    Posted in the Advanced Statistics Forum
    Replies: 16
    Last Post: February 11th 2011, 05:16 AM
  4. Replies: 7
    Last Post: July 25th 2010, 08:26 PM
  5. Probability of being chosen
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 24th 2009, 05:38 PM

Search Tags


/mathhelpforum @mathhelpforum