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

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

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?

Instructions

Tests

tests:
  - text: <code>spiralDiagonals(101)</code> should return a number.
    testString: assert(typeof spiralDiagonals(101) === 'number');
  - text: <code>spiralDiagonals(101)</code> should return 692101.
    testString: assert(spiralDiagonals(101) == 692101);
  - text: <code>spiralDiagonals(303)</code> should return 18591725.
    testString: assert(spiralDiagonals(303) == 18591725);
  - text: <code>spiralDiagonals(505)</code> should return 85986601.
    testString: assert(spiralDiagonals(505) == 85986601);
  - text: <code>spiralDiagonals(1001)</code> should return 669171001.
    testString: assert(spiralDiagonals(1001) == 669171001);

Challenge Seed

function spiralDiagonals(n) {

  return n;
}

spiralDiagonals(1001);

Solution

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;
};