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: Three-Dimensional Plane | Comment 11 of 27 |
(In reply to Three-Dimensional Plane by Ravi Raja)

In the three-dimensional case (which I don't think is actually the problem) your logic about the sphere is just as faulty as in the 2-d case, though in fact factually correct, you haven't proved it.

In the 3-D case, the best way is to expand upon the solution of the 2-d 2-color problem. Instead of a triangle, construct a regular tetrahedron with edges 1 meter long. Then as there are only 3 colors to go around, and there are 4 vertices to a tetrahedron, two vertices must be the same color, and since it's a regular tetrahedron the points are 1 meter apart.
  Posted by Charlie on 2003-05-01 05:32:54

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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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