freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-242-odd-triplets.english.md

id	challengeType	title
5900f45f1000cf542c50ff71	5	Problem 242: Odd Triplets

Description

Given the set {1,2,...,n}, we define f(n,k) as the number of its k-element subsets with an odd sum of elements. For example, f(5,3) = 4, since the set {1,2,3,4,5} has four 3-element subsets having an odd sum of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.

When all three values n, k and f(n,k) are odd, we say that they make an odd-triplet [n,k,f(n,k)].

There are exactly five odd-triplets with n ≤ 10, namely: [1,1,f(1,1) = 1], [5,1,f(5,1) = 3], [5,5,f(5,5) = 1], [9,1,f(9,1) = 5] and [9,9,f(9,9) = 1].

How many odd-triplets are there with n ≤ 1012 ?

Instructions

Tests

tests:
  - text: <code>euler242()</code> should return 997104142249036700.
    testString: assert.strictEqual(euler242(), 997104142249036700, '<code>euler242()</code> should return 997104142249036700.');

Challenge Seed

function euler242() {
  // Good luck!
  return true;
}

euler242();

Solution

// solution required