53 lines
1.1 KiB
Markdown
53 lines
1.1 KiB
Markdown
---
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id: 5900f3b41000cf542c50fec7
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title: 'Problem 72: Counting fractions'
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challengeType: 5
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forumTopicId: 302185
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dashedName: problem-72-counting-fractions
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---
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# --description--
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Consider the fraction, `n`/`d`, where n and d are positive integers. If `n`<`d` and HCF(`n`,`d`)=1, it is called a reduced proper fraction.
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If we list the set of reduced proper fractions for `d` ≤ 8 in ascending order of size, we get:
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<div style='text-align: center;'>1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8</div>
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It can be seen that there are 21 elements in this set.
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How many elements would be contained in the set of reduced proper fractions for `d` ≤ 1,000,000?
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# --hints--
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`countingFractions()` should return a number.
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```js
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assert(typeof countingFractions() === 'number');
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```
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`countingFractions()` should return 303963552391.
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```js
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assert.strictEqual(countingFractions(), 303963552391);
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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 countingFractions() {
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return true;
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}
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countingFractions();
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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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