---
id: 5900f45f1000cf542c50ff71
title: 'Problem 242: Odd Triplets'
challengeType: 5
forumTopicId: 301889
dashedName: 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 ?

# --hints--

`euler242()` should return 997104142249036700.

```js
assert.strictEqual(euler242(), 997104142249036700);
```

# --seed--

## --seed-contents--

```js
function euler242() {

  return true;
}

euler242();
```

# --solutions--

```js
// solution required
```