2018-09-30 22:01:58 +00:00
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---
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id: 5900f3b81000cf542c50fecb
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title: 'Problem 76: Counting summations'
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2020-11-27 18:02:05 +00:00
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challengeType: 5
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2019-08-05 16:17:33 +00:00
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forumTopicId: 302189
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2021-01-13 02:31:00 +00:00
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dashedName: problem-76-counting-summations
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2018-09-30 22:01:58 +00:00
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---
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2020-11-27 18:02:05 +00:00
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# --description--
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2020-02-28 12:39:47 +00:00
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2018-09-30 22:01:58 +00:00
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It is possible to write five as a sum in exactly six different ways:
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2020-02-28 12:39:47 +00:00
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<div style='margin-left: 4em;'>
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4 + 1<br>
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3 + 2<br>
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3 + 1 + 1<br>
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2 + 2 + 1<br>
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2 + 1 + 1 + 1<br>
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1 + 1 + 1 + 1 + 1<br>
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</div>
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2018-09-30 22:01:58 +00:00
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How many different ways can one hundred be written as a sum of at least two positive integers?
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2020-02-28 12:39:47 +00:00
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2020-11-27 18:02:05 +00:00
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# --hints--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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`countingSummations()` should return a number.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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assert(typeof countingSummations() === 'number');
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```
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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`countingSummations()` should return 190569291.
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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```js
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assert.strictEqual(countingSummations(), 190569291);
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --seed--
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2018-09-30 22:01:58 +00:00
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2020-11-27 18:02:05 +00:00
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## --seed-contents--
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2018-09-30 22:01:58 +00:00
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```js
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2020-02-28 12:39:47 +00:00
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function countingSummations() {
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2020-09-15 16:57:40 +00:00
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2018-09-30 22:01:58 +00:00
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return true;
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}
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2020-02-28 12:39:47 +00:00
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countingSummations();
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2018-09-30 22:01:58 +00:00
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```
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2020-11-27 18:02:05 +00:00
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# --solutions--
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2018-09-30 22:01:58 +00:00
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```js
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// solution required
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```
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