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?

 1 

#include 

<

iostream

>

 2 

using

 

namespace

 std;

 3 

 4 

int

 main()

 5 

{

 6 

    

int

 sum 

=

 

1

;

 7 

    

for

(

int

 i

=

3

; i

<=

1001

; i

=

i

+

2

)

 8 

    {

 9 

        

//

top-right

10 

        sum 

+=

 i

*

i;

11 

12 

        

//

top-left

13 

        sum 

+=

 i

*

i

-

i

+

1

;

14 

15 

        

//

bottom-left

16 

        sum 

+=

 i

*

i

-

2

*

i

+

2

;

17 

18 

        

//

bottom-right

19 

        sum 

+=

 i

*

i

-

3

*

i

+

3

;

20 

    }

21 

22 

    cout 

<<

 sum 

<<

 endl;

23 

    cin.

get

();

24 

    

return

 

0

;

25 

}