45 lines
1.0 KiB
Markdown
45 lines
1.0 KiB
Markdown
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---
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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 = 12:1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12 , 7/12 , 8/12 , 9/12 , 10/12 , 11/12 .
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We shall call a fraction that cannot be cancelled down a resilient fraction. 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) = 4/11 . In fact, d = 12 is the smallest denominator having a resilience R(d) < 4/10 .
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Find the smallest denominator d, having a resilience R(d) < 15499/94744 .
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# --hints--
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`euler243()` should return 892371480.
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```js
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assert.strictEqual(euler243(), 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 euler243() {
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return true;
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}
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euler243();
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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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