49 lines
1.4 KiB
Markdown
49 lines
1.4 KiB
Markdown
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---
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id: 5900f4eb1000cf542c50fffd
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title: 'Problem 382: Generating polygons'
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challengeType: 5
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forumTopicId: 302046
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dashedName: problem-382-generating-polygons
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---
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# --description--
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A polygon is a flat shape consisting of straight line segments that are joined to form a closed chain or circuit. A polygon consists of at least three sides and does not self-intersect.
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A set S of positive numbers is said to generate a polygon P if: no two sides of P are the same length, the length of every side of P is in S, and S contains no other value.
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For example: The set {3, 4, 5} generates a polygon with sides 3, 4, and 5 (a triangle). The set {6, 9, 11, 24} generates a polygon with sides 6, 9, 11, and 24 (a quadrilateral). The sets {1, 2, 3} and {2, 3, 4, 9} do not generate any polygon at all.
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Consider the sequence s, defined as follows:s1 = 1, s2 = 2, s3 = 3 sn = sn-1 + sn-3 for n > 3.
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Let Un be the set {s1, s2, ..., sn}. For example, U10 = {1, 2, 3, 4, 6, 9, 13, 19, 28, 41}. Let f(n) be the number of subsets of Un which generate at least one polygon. For example, f(5) = 7, f(10) = 501 and f(25) = 18635853.
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Find the last 9 digits of f(1018).
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# --hints--
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`euler382()` should return 697003956.
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```js
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assert.strictEqual(euler382(), 697003956);
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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 euler382() {
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return true;
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}
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euler382();
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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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