79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
67 lines
1.1 KiB
Markdown
67 lines
1.1 KiB
Markdown
---
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id: 5900f51d1000cf542c51002f
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challengeType: 5
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title: 'Problem 433: Steps in Euclid''s algorithm'
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---
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## Description
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<section id='description'>
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Let E(x0, y0) be the number of steps it takes to determine the greatest common divisor of x0 and y0 with Euclid's algorithm. More formally:x1 = y0, y1 = x0 mod y0xn = yn-1, yn = xn-1 mod yn-1
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E(x0, y0) is the smallest n such that yn = 0.
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We have E(1,1) = 1, E(10,6) = 3 and E(6,10) = 4.
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Define S(N) as the sum of E(x,y) for 1 ≤ x,y ≤ N.
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We have S(1) = 1, S(10) = 221 and S(100) = 39826.
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Find S(5·106).
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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>euler433()</code> should return 326624372659664.
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testString: assert.strictEqual(euler433(), 326624372659664, '<code>euler433()</code> should return 326624372659664.');
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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 euler433() {
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// Good luck!
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return true;
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}
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euler433();
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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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