84 lines
1.9 KiB
Markdown
84 lines
1.9 KiB
Markdown
---
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id: 5900f3881000cf542c50fe9b
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title: 'Problem 28: Number spiral diagonals'
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challengeType: 5
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forumTopicId: 301930
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dashedName: problem-28-number-spiral-diagonals
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---
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# --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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<div style='padding-left: 4em;'>
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<div style='color: red; display: inline;'>21</div> 22 23 24 <div style='color: red; display: inline;'>25</div><br>
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20 <div style='color: red; display: inline;'>7</div> 8 <div style='color: red; display: inline;'>9</div> 10<br>
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19 6 <div style='color: red; display: inline;'>1</div> 2 11<br>
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18 <div style='color: red; display: inline;'>5</div> 4 <div style='color: red; display: inline;'>3</div> 12<br>
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<div style='color: red; display: inline;'>17</div> 16 15 14 <div style='color: red; display: inline;'>13</div><br>
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</div>
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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 an `n` by `n` spiral formed in the same way?
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# --hints--
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`spiralDiagonals(101)` should return a number.
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```js
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assert(typeof spiralDiagonals(101) === 'number');
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```
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`spiralDiagonals(101)` should return 692101.
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```js
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assert(spiralDiagonals(101) == 692101);
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```
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`spiralDiagonals(303)` should return 18591725.
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```js
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assert(spiralDiagonals(303) == 18591725);
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```
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`spiralDiagonals(505)` should return 85986601.
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```js
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assert(spiralDiagonals(505) == 85986601);
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```
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`spiralDiagonals(1001)` should return 669171001.
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```js
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assert(spiralDiagonals(1001) == 669171001);
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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 spiralDiagonals(n) {
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return n;
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}
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spiralDiagonals(1001);
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```
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# --solutions--
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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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