67de105117
* fix: clean-up Project Euler 241-260 * fix: typo * Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-255-rounded-square-roots.md Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.2 KiB
Markdown
51 lines
1.2 KiB
Markdown
---
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id: 5900f4601000cf542c50ff73
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title: 'Problem 243: Resilience'
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challengeType: 5
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forumTopicId: 301890
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dashedName: problem-243-resilience
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---
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# --description--
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A positive fraction whose numerator is less than its denominator is called a proper fraction.
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For any denominator, $d$, there will be $d−1$ proper fractions; for example, with $d = 12$:
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$$\frac{1}{12}, \frac{2}{12}, \frac{3}{12}, \frac{4}{12}, \frac{5}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{9}{12}, \frac{10}{12}, \frac{11}{12}$$
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We shall call a fraction that cannot be cancelled down a resilient fraction.
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Furthermore we shall define the resilience of a denominator, $R(d)$, to be the ratio of its proper fractions that are resilient; for example, $R(12) = \frac{4}{11}$.
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In fact, $d = 12$ is the smallest denominator having a resilience $R(d) < \frac{4}{10}$.
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Find the smallest denominator $d$, having a resilience $R(d) < \frac{15\\,499}{94\\,744}$.
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# --hints--
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`resilience()` should return `892371480`.
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```js
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assert.strictEqual(resilience(), 892371480);
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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 resilience() {
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return true;
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}
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resilience();
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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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