freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-28-number-spiral-diagonals.md

id	title	challengeType	forumTopicId	dashedName
5900f3881000cf542c50fe9b	Problem 28: Number spiral diagonals	5	301930	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.

assert(typeof spiralDiagonals(101) === 'number');

spiralDiagonals(101) should return 692101.

assert(spiralDiagonals(101) == 692101);

spiralDiagonals(303) should return 18591725.

assert(spiralDiagonals(303) == 18591725);

spiralDiagonals(505) should return 85986601.

assert(spiralDiagonals(505) == 85986601);

spiralDiagonals(1001) should return 669171001.

assert(spiralDiagonals(1001) == 669171001);

--seed--

--seed-contents--

function spiralDiagonals(n) {

  return n;
}

spiralDiagonals(1001);

--solutions--

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;
};