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Paradoxical

Weekly Problem 41 - 2007
The Queen of Spades always lies for the whole day or tells the truth for the whole day. Which of these statements can she never say?

Proximity

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. More information on many of our other activities can be found here.
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