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Combinatorics 6.0/10

Three-Colour Bracelets

A bracelet consists of 6 beads equally spaced on a circular loop, each bead red, green or blue (not every colour need be used). Two bracelets are the same if one can be rotated and/or flipped over to match the other. How many different bracelets are there? Give an integer.

Related problems & prerequisites

Worth solving first

Source: Standard application of Burnside's lemma; no traceable original source. Statement written for AxiomIQ.