All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
2 Colors 2 (Posted on 2003-08-25) Difficulty: 4 of 5
Suppose you have an infinite plane, and each point on the plane has been arbitrarily painted one of two colors.

Prove that there exists an equilateral triangle whose vertices are all the same color.

What is the fewest number of points needed to prove this?

See The Solution Submitted by DJ    
Rating: 4.3684 (19 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): 5-point proof - to DJ | Comment 11 of 14 |
(In reply to re(2): 5-point proof - to DJ by aln)

The proof involves not randomly choosing two points, but choosing whatever two points are necessary to get the sought triangle. If in fact all the points are the same color (it's really a 1-color plane) then every triangle has vertices all the same color. But if the plane has two colors, it is possible to select two points of different colors. The key is select, not randomly.
  Posted by Charlie on 2003-09-21 16:34:10

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information