freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-265-binary-circles.english.md

id, challengeType, title

id	challengeType	title
5900f4761000cf542c50ff88	5	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

tests:
  - text: <code>euler265()</code> should return 209110240768.
    testString: assert.strictEqual(euler265(), 209110240768, '<code>euler265()</code> should return 209110240768.');

Challenge Seed

function euler265() {
  // Good luck!
  return true;
}

euler265();

Solution

// solution required