**Problem:**

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 1001 by 1001 spiral formed in the same way?

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 1001 by 1001 spiral formed in the same way?

**Solution:**

669171001

**Code:**

The solution may include methods that will be found here: Library.java .

The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/*

* Solution to Project Euler problem 28

* By Nayuki Minase

*

* http://nayuki.eigenstate.org/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*/

public final class p028 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p028().run());

}

/*

* From the diagram, let's observe the four corners of an n * n square (where n is odd).

* It's not hard to convince yourself that the top right corner always has the value n^2.

* Working counterclockwise (backwards), the top left corner has the value n^2 - (n - 1),

* the bottom left corner has the value n^2 - 2(n - 1), and the bottom right is n^2 - 3(n - 1).

* Putting it all together, this outermost ring contributes 4n^2 - 6(n - 1) to the final sum.

*

* Incidentally, the closed form of this sum is (4m^3 + 3m^2 + 8m - 9) / 6, where m = size.

*/

private static final int SIZE = 1001; // Must be odd

public String run() {

long sum = 1; // Special case for size 1

for (int n = 3; n <= SIZE; n += 2)

sum += 4 * n * n - 6 * (n - 1);

return Long.toString(sum);

}

}

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