79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
80 lines
1.8 KiB
Markdown
80 lines
1.8 KiB
Markdown
---
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id: 5900f3881000cf542c50fe9b
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challengeType: 5
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title: 'Problem 28: Number spiral diagonals'
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---
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## Description
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<section id='description'>
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Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
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21 22 23 24 25
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20 7 8 9 10
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19 6 1 2 11
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18 5 4 3 12
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17 16 15 14 13
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It can be verified that the sum of the numbers on the diagonals is 101.
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What is the sum of the numbers on the diagonals in a n by n spiral formed in the same way?
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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>spiralDiagonals(101)</code> should return 692101.
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testString: assert(spiralDiagonals(101) == 692101, '<code>spiralDiagonals(101)</code> should return 692101.');
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- text: <code>spiralDiagonals(303)</code> should return 18591725.
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testString: assert(spiralDiagonals(303) == 18591725, '<code>spiralDiagonals(303)</code> should return 18591725.');
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- text: <code>spiralDiagonals(505)</code> should return 85986601.
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testString: assert(spiralDiagonals(505) == 85986601, '<code>spiralDiagonals(505)</code> should return 85986601.');
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- text: <code>spiralDiagonals(1001)</code> should return 669171001.
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testString: assert(spiralDiagonals(1001) == 669171001, '<code>spiralDiagonals(1001)</code> should return 669171001.');
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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 spiralDiagonals(n) {
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// Good luck!
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return n;
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}
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spiralDiagonals(1001);
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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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const spiralDiagonals = (n) => {
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const Sn2 = (n) => {
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return n*(n+1)*(2*n+1)/6;
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};
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const Sn = (n) => {
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return n*(n+1)/2;
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};
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let sum = (Sn2(n-1) + Sn(n-1) + n-1) + (Math.floor(n/2) + Sn2(n));
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return sum;
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};
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```
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</section>
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