Primitive Necklaces
A necklace of 12 beads, each black or white, is considered up to rotation. Call it primitive if no rotation other than the identity maps it to itself (equivalently, it does not consist of a shorter block repeated). How many primitive necklaces of 12 beads are there? Give an integer.
Related problems & prerequisites
Worth solving first
- Balanced Necklaces 6.0/10
- Three-Colour Bracelets 6.0/10
- Rotating a Three-by-Three Grid 6.0/10
Source: Counting aperiodic necklaces (Lyndon words) by Mobius inversion; standard material in combinatorics on words. Statement written for AxiomIQ.