[ZT+FY]欧拉工程265

欧拉工程265

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2^N binary digits can be placed in a circle so that all the N-digit clockwise subsequences are distinct.

2^N位二进制数字能够组成这样一个环，任意N位顺时针旋转会组成不同的序列。

For N=3, two such circular arrangements are possible, ignoring rotations:

例如，N=3，如下两个圆环，忽略旋转：

For the first arrangement, the 3-digit subsequences, in clockwise order, are:

第一个环，按照3bit组合，得到如下序列：

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:

每个循环都可以利用链接比特位来编码成开始元素位均为0的码序列。对于N = 3有23和29两种排法：

00010111 = 23

00011101 = 29

Calling S(N) the sum of the unique numeric representations, we can see that S(3) = 23 + 29 = 52.

设定S(N)为这些排法十进制的和，我们能够得出S(3) = 23+29 = 52；

Find S(5).

试着求一下S(5)吧。

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