Proximity

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

 

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
 
If you're stuck, try this proof sorting activity.
Image
Proximity

 



 

This problem was taken from the Hungarian magazine KoMaL. There are many other challenging problems in English on the KoMal website.