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

Home > Shapes
3 colors (Posted on 2003-05-01) Difficulty: 3 of 5
Imagine that a painter went down to a mathematical plane and colored all of the points on that plane one of three colors.

Prove that there exist two points on this plane, exactly one meter apart, that have the same color.

See The Solution Submitted by Jonathan Waltz    
Rating: 4.1000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Elegant proof | Comment 19 of 28 |
Consider two points in cartesian space: A (0,0) and B (√3,0), where one unit equals 1m of distance. Points C (√3/2,1/2) and D (√3/2,-1/2) are each 1m from both A and B, and C and D are 1m from each other.

If A and B are different colors, both C and D will be the third color, and will satisfy the condition that two points 1m apart are the same color. To avoid the situation where two points √3m apart are different colors, for a given point, every point √3m from it would have to be the same color as the center point, in which case two points 1m apart on the resulting circle will satisfy the condition.
  Posted by Bryan on 2003-05-01 13:01:09

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 (12)
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