Stage: 4 Challenge Level: 
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We are given a regular icosahedron having three red
vertices. Show that it has a vertex that has at least
two red neighbours.
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Patterned numbers. Manipulating algebraic expressions/formulae. Inequality/inequalities. Dynamical systems. Mathematical reasoning & proof. Visualising. Icosahedra. Generalising. Proof by contradiction. Number theory.
Published September 2000,February 2010.
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