# The sum of squares and the square of sums

Published on 2011-07-21Project Euler #6 has been answered more times than problems 3-5, which is generally interpreted as meaning that it's easier than they. It reads:

The sum of the squares of the first ten natural numbers is,

1

^{2}+ 2^{2}+ ... + 10^{2}= 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + ... + 10)

^{2}= 55^{2}= 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

100 is definitely low enough to allow a brute-force solution, so that's how I approached the problem. Two variables churned through a single, 100-iteration for loop.

using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace Problem6 { class Program { static void Main(string[] args) { int sumOfSquares = 0; long squareOfSums = 0; for (int i = 1; i <= 100; i++) { sumOfSquares += (i * i); squareOfSums += i; } squareOfSums *= squareOfSums; Console.WriteLine("Difference: {0}",(squareOfSums - sumOfSquares)); } } }