Results 1 to 2 of 2

Math Help - Discrete math set question someone help?? thank you

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    3

    Discrete math set question someone help?? thank you

    In a period of 4 weeks, Joe played tennis every day. He plays at least one set everyday, and played a total of 40 sets. (In each day the nubmer of sets Joe played is an integer.) Show that there is a consecutive span of days during which Joe played exactly 15 sets of tennis.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by peiyilee View Post
    In a period of 4 weeks, Joe played tennis every day. He plays at least one set everyday, and played a total of 40 sets. Show that there is a consecutive span of days during which Joe played exactly 15 sets of tennis.
    Suppose that S_k is the sum total of all sets completed at the end of the kth day.
    Thus 1 \le S_1  < S_2  <  \cdots  < S_{27}  < S_{28}  = 40. That is a set of 28 different sums.
    Construct a new set of 28 different sums, S_1  + 15 < S_2  + 15 <  \cdots  < S_{27}  + 15 < S_{28}  + 15 = 55.
    Now we have 56 representations of numbers 1 to 55.
    Use the pigeonhole principle to conclude.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Discrete/CS math question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 12th 2010, 03:23 AM
  2. Discrete math question about sets.
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 23rd 2009, 07:05 PM
  3. Discrete Math question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 24th 2009, 07:05 PM
  4. discrete math question please help
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 15th 2008, 12:34 PM
  5. Discrete Math/Geometry Question Help!
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 12th 2007, 06:38 AM

Search Tags


/mathhelpforum @mathhelpforum