Two-color necklaces

How many distinct necklaces of 44 beads can be made with 22 colors, where rotations are considered identical?

Show hints (2)+
  1. Use Burnside's lemma over the cyclic rotation group.
  2. A rotation fixes 2gcd(shift,4)2^{\gcd(\text{shift},4)} colorings.

Answer

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6

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Asked at: Jane Street, Two Sigma

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