2018-10-10 22:03:03 +00:00
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---
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id: 5900f45f1000cf542c50ff71
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2020-12-16 07:37:30 +00:00
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title: 问题242:奇数三胞胎
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-242-odd-triplets
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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给定集合{1,2,...,n},我们将f(n,k)定义为具有奇数元素之和的k元素子集的数量。例如,f(5,3)= 4,因为集合{1,2,3,4,5}有四个3元素子集具有奇数元素,即:{1,2,4},{ 1,3,5},{2,3,4}和{2,4,5}。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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当所有三个值n,k和f(n,k)都是奇数时,我们说它们产生奇数三元组\[n,k,f(n,k)]。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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正好有五个奇数三元组,n≤10,即:\[1,1,f(1,1)= 1],\[5,1,f(5,1)= 3],\[5,5,f (5,5)= 1],\[9,1,f(9,1)= 5]和\[9,9,f(9,9)= 1]。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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n≤1012,有多少奇数三胞胎?
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler242()`应该返回997104142249036700。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler242(), 997104142249036700);
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2018-10-10 22:03:03 +00:00
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```
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2021-01-13 02:31:00 +00:00
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# --seed--
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## --seed-contents--
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```js
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function euler242() {
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return true;
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}
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euler242();
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```
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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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```js
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// solution required
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```
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