# Problem 265: Binary Circles
2N binary digits can be placed in a circle so that all the N-digit
clockwise subsequences are distinct. For N=3, two such circular
arrangements are possible, ignoring rotations: For the first
arrangement, the 3-digit subsequences, in clockwise order, are: 000,
001, 010, 101, 011, 111, 110 and 100. Each 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: 00010111 2 = 23 00011101 2 = 29 Calling S(N) the sum of the unique
numeric representations, we can see that S(3) = 23 + 29 = 52. Find S(5).