Project Euler : Sum Of Both Diagonals In A 1001 By 1001 Spiral

This one I solved using just paper and pencil, and am happy about it. All that was required was a keen observation on how the numbers along the diagonal form out of the previous number. Lets take a look at one of the diagonals of the 5 x 5 spiral

21     22     23     24     25

20     07     08     09     10

19     06     01     02     11

18     05     04     03     12

17     16     15     14     13

Consider the numbers along the diagonal originating in the center at 01 moving towards the upper right corner. The numbers are 01, 09, 25. Let me tell you that the next number along this diagonal will be 49. Do you see any pattern emerging yet?

Well, all these number are squares -

Considering the distance of the number from the center of the spiral as a parameter, this series can be written as:

The numbers along the other diagonals are simply derived from by subtracting certain values.

Now, all that the problem asks us to do is to sum up the numbers for .

for

This is a simple summing up exercise. Solved !!

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