chore(i18n,learn): processed translations (#44851)

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---
id: 5900f4761000cf542c50ff88
title: 'Problem 265: Binary Circles'
challengeType: 5
forumTopicId: 301914
dashedName: problem-265-binary-circles
---
# --description--
$2^N$ 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:
<img class="img-responsive center-block" alt="two circular arrangements for N = 3" src="https://cdn.freecodecamp.org/curriculum/project-euler/binary-circles.gif" style="background-color: white; padding: 10px;" />
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--
`binaryCircles()` should return `209110240768`.
```js
assert.strictEqual(binaryCircles(), 209110240768);
```
# --seed--
## --seed-contents--
```js
function binaryCircles() {
return true;
}
binaryCircles();
```
# --solutions--
```js
// solution required
```