---
id: 5900f4761000cf542c50ff88
challengeType: 5
title: 'Problem 265: Binary Circles'
---
## Description
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).
## Instructions
## Tests
```yml
tests:
- text: euler265() should return 209110240768.
testString: assert.strictEqual(euler265(), 209110240768, 'euler265() should return 209110240768.');
```
## Challenge Seed
```js
function euler265() {
// Good luck!
return true;
}
euler265();
```