Editing Necklace problem (section)

== Formulation ==
The necklace problem involves the reconstruction of a [[Necklace (combinatorics)|necklace]] of <math>n</math> beads, each of which is either black or white, from partial information. The information specifies how many copies the necklace contains of each possible arrangement of <math>k</math> black beads. For instance, for <math>k=2</math>, the specified information gives the number of pairs of black beads that are separated by <math>i</math> positions, for <math>i=0,\dots, \lfloor n/2-1 \rfloor </math>.
This can be made formal by defining a <math>k</math>-configuration to be a necklace of <math>k</math> black beads and <math>n-k</math> white beads, and counting the number of ways of rotating a <math>k</math>-configuration so that each of its black beads coincides with one of the black beads of the given necklace.

The necklace problem asks: if <math>n</math> is given, and the numbers of copies of each <math>k</math>-configuration are known up to some threshold <math>k\le K</math>, how large does the threshold <math>K</math> need to be before this information completely determines the necklace that it describes? Equivalently, if the information about <math>k</math>-configurations is provided in stages, where the <math>k</math>th stage provides the numbers of copies of each <math>k</math>-configuration, how many stages are needed (in the worst case) in order to reconstruct the precise pattern of black and white beads in the original necklace?