yaworsw/euler-manager

---
:id: 265
:name: Binary Circles
:url: https://projecteuler.net/problem=265
:content: "2<sup>N</sup> binary digits can be placed in a circle so that all the N-digit
  clockwise subsequences are distinct.\n\nFor N=3, two such circular arrangements
  are possible, ignoring rotations:\n\n ![p265_BinaryCircles.gif]({{ images_dir }}/p265_BinaryCircles.gif)\n\nFor
  the first arrangement, the 3-digit subsequences, in clockwise order, are:  \n 000,
  001, 010, 101, 011, 111, 110 and 100.\n\nEach circular arrangement can be encoded
  as a number by concatenating the binary digits starting with the subsequence of
  all zeros as the most significant bits and proceeding clockwise. The two arrangements
  for N=3 are thus represented as 23 and 29:\n\n00010111 <sub>2</sub> = 23\n\n00011101 <sub>2</sub>
  = 29\n\nCalling S(N) the sum of the unique numeric representations, we can see that
  S(3) = 23 + 29 = 52.\n\nFind S(5).\n\n"