45 lines
1.0 KiB
Markdown
45 lines
1.0 KiB
Markdown
---
|
||
id: 5900f4601000cf542c50ff73
|
||
title: 'Problem 243: Resilience'
|
||
challengeType: 5
|
||
forumTopicId: 301890
|
||
dashedName: problem-243-resilience
|
||
---
|
||
|
||
# --description--
|
||
|
||
A positive fraction whose numerator is less than its denominator is called a proper fraction.
|
||
|
||
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 .
|
||
|
||
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 .
|
||
|
||
Find the smallest denominator d, having a resilience R(d) < 15499/94744 .
|
||
|
||
# --hints--
|
||
|
||
`euler243()` should return 892371480.
|
||
|
||
```js
|
||
assert.strictEqual(euler243(), 892371480);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function euler243() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler243();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|