Results 1 to 2 of 2

Math Help - Interesting Question

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    57

    Interesting Question

    I am working on some supplemental math problems and this question has me boggled. Any push in the right direction would be appreciated on how to start this.

    Show that in a group of five people (where any two people are mutual friends or enemies) there are not necessarily three mutual friends or three mutual enemies.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by vexiked View Post
    I am working on some supplemental math problems and this question has me boggled. Any push in the right direction would be appreciated on how to start this.

    Show that in a group of five people (where any two people are mutual friends or enemies) there are not necessarily three mutual friends or three mutual enemies.
    You just have to come up with an example that shows this can happen.

    Here is an alternative formulation that you may find useful: Suppose you have a graph with 5 nodes, in which every node is connected to every other node. See if you can find a way to color the arcs with two colors (red and blue, say) so that there is no triangle (three nodes and their connecting arcs) with all its arcs the same color.

    The 5 nodes correspond to the 5 people and the colors correspond to friendship or its opposite.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. interesting question
    Posted in the Business Math Forum
    Replies: 1
    Last Post: October 1st 2010, 12:26 AM
  2. interesting question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 8th 2010, 01:41 PM
  3. Interesting question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 22nd 2009, 07:02 PM
  4. Interesting Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 12th 2008, 06:26 PM
  5. interesting question
    Posted in the Advanced Applied Math Forum
    Replies: 7
    Last Post: October 11th 2007, 10:48 PM

Search Tags


/mathhelpforum @mathhelpforum