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