2018-10-10 22:03:03 +00:00
---
id: 5900f45f1000cf542c50ff71
2021-02-06 04:42:36 +00:00
title: 'Problem 242: Odd Triplets'
2018-10-10 22:03:03 +00:00
challengeType: 5
2021-02-06 04:42:36 +00:00
forumTopicId: 301889
2021-01-13 02:31:00 +00:00
dashedName: problem-242-odd-triplets
2018-10-10 22:03:03 +00:00
---
2020-12-16 07:37:30 +00:00
# --description--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
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}.
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
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)].
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
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].
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
How many odd-triplets are there with n ≤ 1012 ?
2018-10-10 22:03:03 +00:00
2020-12-16 07:37:30 +00:00
# --hints--
2018-10-10 22:03:03 +00:00
2021-02-06 04:42:36 +00:00
`euler242()` should return 997104142249036700.
2018-10-10 22:03:03 +00:00
```js
2020-12-16 07:37:30 +00:00
assert.strictEqual(euler242(), 997104142249036700);
2018-10-10 22:03:03 +00:00
```
2021-01-13 02:31:00 +00:00
# --seed--
## --seed-contents--
```js
function euler242() {
return true;
}
euler242();
```
2020-12-16 07:37:30 +00:00
# --solutions--
2020-08-13 15:24:35 +00:00
2021-01-13 02:31:00 +00:00
```js
// solution required
```