Abstract. There is a famous problem which involves discriminating the faces of a die using 3 colors: how many different patterns can be produced? This article introduces Burnside's lemma which is a powerful method for handling such problems. It requires a knowledge of group theory, but is not so difficult and is likely to be understood by elementary school pupils.

Received: September 25, 2012

AMS Subject Classification: 19A22, 00A09, 97A20

Key Words and Phrases: Burnside's counting theorem, Pólya's formula, permutation, orbit, invariant, equivalence, equivalence class

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