9459

Among Six People, Either Three Know Each Other or Three Are Strangers to Each Other

Represent the six people as the vertices of a regular hexagon. Draw a blue segment between a pair of vertices if the corresponding pair of people know each other and otherwise draw a red segment. A triangle with all three sides of the same color is called monochromatic; fill in such triangles with the appropriate color. There is always a monochromatic triangle! Moreover, there are always two monochromatic triangles!

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

See Chapter 13 of [1] and in particular, exercise 20, p. 300.
Reference
[1] M. Bóna, A Walk Through Combinatorics, 2nd. ed., Singapore: World Scientific, 2006.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+