### Project Euler - Problem 28

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 a 1001 by 1001 spiral formed in the same way?

Solution

//calculates the sum for the level of the square
//each increase in level only requires calculating 4 new values, the corners
let levelValue (start:int) (side:int) =
let diffAtLevel = side - 1
let sum = (start + diffAtLevel) + (start + (diffAtLevel * 2)) + (start + (diffAtLevel * 3)) + (start + (diffAtLevel * 4))
sum

//recursively iterates from level 0, which is the center
//to the outer part of the array
//and for each level calculates the additional sum and sums that to running sum
let rec sumByPowers start priorLevelSquared level endSide sum =
if level > endSide then
sum
else
let newSum = sum + levelValue priorLevelSquared level
sumByPowers start (level * level) (level + 2) endSide newSum

let resultTest = sumByPowers 0 0 1 1001 1