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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-265-binary-circles.md

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+---
+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
+```