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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-243-resilience.md

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+---
+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
+```