---
id: 5900f3881000cf542c50fe9b
title: 'Problem 28: Number spiral diagonals'
challengeType: 5
forumTopicId: 301930
dashedName: problem-28-number-spiral-diagonals
---
# --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 an `n` by `n` spiral formed in the same way?
# --hints--
`spiralDiagonals(101)` should return a number.
```js
assert(typeof spiralDiagonals(101) === 'number');
```
`spiralDiagonals(101)` should return 692101.
```js
assert(spiralDiagonals(101) == 692101);
```
`spiralDiagonals(303)` should return 18591725.
```js
assert(spiralDiagonals(303) == 18591725);
```
`spiralDiagonals(505)` should return 85986601.
```js
assert(spiralDiagonals(505) == 85986601);
```
`spiralDiagonals(1001)` should return 669171001.
```js
assert(spiralDiagonals(1001) == 669171001);
```
# --seed--
## --seed-contents--
```js
function spiralDiagonals(n) {
return n;
}
spiralDiagonals(1001);
```
# --solutions--
```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;
};
```