Combinatorics · Counting up to symmetry · Rotations · Necklaces · Compositions · Case analysis
Four vertices of a given regular octagon are to be coloured blue and the remaining four red. Two colourings are called equivalent if one of them is carried onto the other by a rotation of the octagon about its centre, that is, if some such rotation sends every vertex to a vertex of the same colour. How many pairwise non-equivalent colourings are there?
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Serbian Regional Competition (Okruzno takmicenje) 2001, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source