Solution
Two-Color Necklaces
Show the problem again
How many distinct necklaces can be made from 6 beads, each black or white, where two necklaces are considered the same if one is a rotation of the other?
Worked solution
The answer is 14. By Burnside's lemma, count colorings fixed by each of the 6 rotations and average. A rotation by k positions fixes 2^gcd(k,6) colorings: k = 0, ..., 5 gives 64, 2, 4, 8, 4, 2, summing to 84. Dividing by 6 yields 84/6 = 14 distinct necklaces.
Source: Necklace counting by Burnside's lemma and Polya enumeration; standard material in enumerative combinatorics. Statement written for AxiomIQ.