70 lines
1.5 KiB
Markdown
70 lines
1.5 KiB
Markdown
---
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id: 5900f3b61000cf542c50fec8
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challengeType: 5
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title: 'Problem 73: Counting fractions in a range'
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forumTopicId: 302186
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---
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## Description
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<section id='description'>
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Consider the fraction, <var>n</var>/<var>d</var>, where n and d are positive integers. If <var>n</var><<var>d</var> and HCF(<var>n</var>,<var>d</var>)=1, it is called a reduced proper fraction.
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If we list the set of reduced proper fractions for <var>d</var> ≤ 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, <strong>3/8</strong>, <strong>2/5</strong>, <strong>3/7</strong>, 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 3 fractions between 1/3 and 1/2.
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How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for <var>d</var> ≤ 12,000?
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>countingFractionsInARange()</code> should return a number.
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testString: assert(typeof countingFractionsInARange() === 'number');
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- text: <code>countingFractionsInARange()</code> should return 7295372.
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testString: assert.strictEqual(countingFractionsInARange(), 7295372);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function countingFractionsInARange() {
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return true;
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}
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countingFractionsInARange();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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