Proximity

Age 14 to 16 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.

If you're stuck, try this proof sorting activity.
 icosahedron



 

This problem was taken from the Hungarian magazine KoMaL. There are many other challenging problems in English on the KoMal website.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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