Stage: 4 Challenge Level: 
|
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
|
 |
This problem was taken from the Hungarian magazine KoMaL. There are many other challenging problems in English on the KoMal website.
Number theory. Patterned numbers. Inequality/inequalities. Icosahedra. Visualising. Manipulating algebraic expressions/formulae. Mathematical reasoning & proof. Proof Sorting. Proof by contradiction. Stage 5 - Reviewed 2012.
Published September 2000.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk