45 lines
1.1 KiB
Markdown
45 lines
1.1 KiB
Markdown
---
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id: 5900f45f1000cf542c50ff71
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title: 'Problem 242: Odd Triplets'
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challengeType: 5
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forumTopicId: 301889
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dashedName: problem-242-odd-triplets
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---
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# --description--
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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 an odd-triplet $[n, k, f(n, k)]$.
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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 $[9, 9, f(9, 9) = 1]$.
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How many odd-triplets are there with $n ≤ {10}^{12}$?
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# --hints--
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`oddTriplets()` should return `997104142249036700`.
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```js
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assert.strictEqual(oddTriplets(), 997104142249036700);
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```
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# --seed--
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## --seed-contents--
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```js
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function oddTriplets() {
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return true;
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}
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oddTriplets();
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```
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# --solutions--
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```js
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// solution required
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```
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