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.)
re: Two-Dimensional Plane | Comment 9 of 27 |
(In reply to Two-Dimensional Plane by Ravi Raja)

Apparently you and I were posting at the same time. Again, consider 60-degree arcs along the circumference of alternating color. The endpoints of the arcs are 1 meter apart, and one of the endpoints of any arc is the opposite color as the other, since we always choose to include the endpoint as a specific (ie cw or ccw) end of each arc.
  Posted by Charlie on 2003-05-01 05:29:07

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

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information