22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
77 lines
1.6 KiB
Markdown
77 lines
1.6 KiB
Markdown
---
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id: 5900f53b1000cf542c51004d
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challengeType: 5
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isHidden: false
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title: 'Problem 462: Permutation of 3-smooth numbers'
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forumTopicId: 302137
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---
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## Description
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<section id='description'>
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<!-- TODO use MathJax -->
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A 3-smooth number is an integer which has no prime factor larger than 3. For an integer N, we define S(N) as the set of 3-smooth numbers less than or equal to N . For example, S(20) = { 1, 2, 3, 4, 6, 8, 9, 12, 16, 18 }.
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We define F(N) as the number of permutations of S(N) in which each element comes after all of its proper divisors.
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This is one of the possible permutations for N = 20.
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- 1, 2, 4, 3, 9, 8, 16, 6, 18, 12.
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This is not a valid permutation because 12 comes before its divisor 6.
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- 1, 2, 4, 3, 9, 8, 12, 16, 6, 18.
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We can verify that F(6) = 5, F(8) = 9, F(20) = 450 and F(1000) ≈ 8.8521816557e21.
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Find F(1018). Give as your answer its scientific notation rounded to ten digits after the decimal point.
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When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 112,233,445,566,778,899 then the answer format would be 1.1223344557e17.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler462()</code> should return Infinity.
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testString: assert.strictEqual(euler462(), Infinity);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler462() {
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// Good luck!
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return true;
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}
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euler462();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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