---
id: 5900f4761000cf542c50ff88
title: 'Problem 265: Binary Circles'
challengeType: 5
forumTopicId: 301914
dashedName: 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).

# --hints--

`euler265()` should return 209110240768.

```js
assert.strictEqual(euler265(), 209110240768);
```

# --seed--

## --seed-contents--

```js
function euler265() {

  return true;
}

euler265();
```

# --solutions--

```js
// solution required
```