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 Three-Dimensional Plane | Comment 8 of 28 |
Suppose that the Mathematical Plane is a Three-Dimensional Plane, then we consider a SPHERE of Unit radius. Then there are Infinitely many points lying on the circumference of the sphere, all of which are at Unit distance from the centre of the sphere. Suppose the centre of one color and there is AT LEAST one point on the circumference which is of the same color as that of the centre, then there is nothing left to prove. If suppose the circumference consists entirely of points of ther other two colors ONLY, then obviously there exists AT LEAST one pair of points on the circumference which will satisfy the given conditions.
Hence Proved.
(I do not know whether this reasoning of mine is correct or not. If not then someone please do correct me).
  Posted by Ravi Raja on 2003-05-01 05:27:12
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 (11)
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