Results 1 to 2 of 2

Math Help - hexagons and lines?

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    12

    hexagons and lines?

    I'm really confused as to where to even start with this..
    with a regular hexagon, 2 corners joined by a straight line. The lines are either red or blye. and 15 lines in total. show no matter how the lines are colored there must be a triangle with all 3 edges the same color.
    any advice would be great
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,793
    Thanks
    1688
    Awards
    1
    Quote Originally Posted by gpenguin View Post
    with a regular hexagon, 2 corners joined by a straight line. The lines are either red or blye. and 15 lines in total. show no matter how the lines are colored there must be a triangle with all 3 edges the same color.
    This is a very tedious argument. Read very slowly.
    Call one vertex X. There are five others that we will divide into two sets.
    Set R will be the vertices that are joined to X by a red edge.
    Set B will be the vertices that are joined to X by a blue edge.

    One of those set must contain at least three vertices. Say it is R.
    If one pair of those three vertices is joined by a red side we are done. WHY?
    If all three vertices are joined by blue edges we are also done. HOW?

    How can you finish?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Regular Hexagons and a Circle
    Posted in the Geometry Forum
    Replies: 10
    Last Post: March 29th 2011, 09:30 AM
  2. Replies: 2
    Last Post: April 2nd 2010, 01:14 AM
  3. Magic Hexagons
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: June 10th 2008, 03:44 AM
  4. Hexagons!!!
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 26th 2006, 07:40 AM
  5. hexagons -reeli hard
    Posted in the Geometry Forum
    Replies: 3
    Last Post: May 19th 2006, 04:57 AM

Search Tags


/mathhelpforum @mathhelpforum