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---
id: 5900f45f1000cf542c50ff71
challengeType: 5
title: 'Problem 242: Odd Triplets'
---
## Description
< section id = '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}.
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When all three values n, k and f(n,k) are odd, we say that they make
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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 ?
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## Instructions
< section id = 'instructions' >
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## Tests
< section id = 'tests' >
```yml
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tests:
- text: < code > euler242()</ code > should return 997104142249036700.
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testString: assert.strictEqual(euler242(), 997104142249036700, '< code > euler242()< / code > should return 997104142249036700.');
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```
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## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
function euler242() {
// Good luck!
return true;
}
euler242();
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
// solution required
```
< / section >