ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
1.4 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4eb1000cf542c50fffd | Problem 382: Generating polygons | 5 | 302046 | problem-382-generating-polygons |
--description--
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.
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.
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.
Consider the sequence s, defined as follows:s1 = 1, s2 = 2, s3 = 3 sn = sn-1 + sn-3 for n > 3.
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.
Find the last 9 digits of f(1018).
--hints--
euler382() should return 697003956.
assert.strictEqual(euler382(), 697003956);
--seed--
--seed-contents--
function euler382() {
return true;
}
euler382();
--solutions--
// solution required