It's been my impression so far that taking on Project Euler problems has been made me think more logically and perhaps more thoroughly. I would hesitate before saying that it has made me think more mathematically, as my approach in solving the problems thus far has been to restate them in the formal statements of a computer language and let the processor solve it for me, usually by letting it test all possible answers and then reporting which one was correct. So I thought I would try something with more finesse for problem 9, which reads:

A Pythagorean triplet is a set of three natural numbers, `a` < `b` < `c`, for which `a`2 + `b`2 = `c`2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which `a` + `b` + `c` = 1000.

Find the product `abc`.

I tried to find some way to write something elegant, but I gave up fairly quickly and wrote a brute-force solution so ugly it has a `goto` in it.

```using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Problem9
{
class Program
{
static void Main(string[] args)
{
int[] result = new int;
for (int i = 1; i < 800; i++)
{
for (int j = 1; j < 800; j++)
{
for (int k = 1; k < 800; k++)
{
if ((i + j + k == 1000) && (((j * j) + (i * i)) == (k * k)))
{
result = i;
result = j;
result = k;