Abstract. Place elements in the form of an inverted triangle, and color them from top to bottom by row according to some rule. When doing so, is it possible to predict the color of the element that becomes the triangle's bottom vertex? It turns out that when you begin with a triangle of 4, 10, 28, c elements in its top row, knowing the colors of that row's leftmost and rightmost elements is sufficient to predict the color of that bottom vertex, and this article presents an elegant proof of this surprising result. Coloring triangles is simple even for children, but this problem provides a springboard to learning about some advanced mathematics, including Abelian groups, the superposition principle, and fractal structures.

Received: December 21, 2012

AMS Subject Classification: 00A08, 20K01, 26B40, 28A80

Key Words and Phrases: congruence, Abelian group, superposition principle, fractal

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