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Necklace problem

Moreau's necklace-counting function treats a problem that is not only recreational.


The necklace problem is a problem in recreational mathematics, solved in the early 21st century.

Suppose that a person you are in contact with has a necklace of n beads, each of which is either black or white. You wish to identify in what order the n beads go around the necklace. However, you are only given partial information. At stage k you are told, for each set of k beads, their relative location around the necklace.

The question is: given n, how many stages you will have to go through in order to be able to distinguish any different necklaces?

Alon, Caro, Krasikov and Roditty showed that 1 + log2(n) is sufficient, using a cleverly enhanced inclusion-exclusion principle.

Radcliffe and Scott showed that if n is prime, 3 is sufficient, and for any n, 9 times the number of prime factors of n is sufficient.

Pebody showed that for any n, 6 is sufficient.