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.