Stage: 5 Challenge Level: 
Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.
Mathematical reasoning & proof. Dynamical systems. Inequality/inequalities. Generalising. Visualising. Tetrahedra. Proof by contradiction. Number theory. Patterned numbers. Manipulating algebraic expressions/formulae.
Published November 2002,December 2002.
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