# Pythagorean triplet

Project Euler again, this time its problem 9.

A Pythagorean triplet is a set of three natural numbers, abc, for which:

$a^{2}+b^{2}=c^{2}$

For example:

$3^{2}+4^{2}=9+16=25=5^{2}$.

There exists exactly one Pythagorean triplet for which abc = 1000.
Find the product abc.

My first draft is simply brute force checking:

Module Module1

Sub Main()
Dim beganAt As Date = Now

Dim answer As Integer = pythagorean(1000)

Dim endAt As Global.System.TimeSpan = Now.Subtract(beganAt)
Dim took As Integer = endAt.Milliseconds

Console.WriteLine(answer.ToString + " in " + took.ToString + "ms.")
End Sub

Private Function pythagorean(ByVal thisNumber As Integer) As Integer
For a As Integer = 1 To thisNumber
For b As Integer = 1 To thisNumber
For c As Integer = 1 To thisNumber
If a + b + c = 1000 Then
If (a * a) + (b * b) = (c * c) Then
Return (a * b * c)
End If
End If
Next
Next
Next
Return -1
End Function

End Module

It takes 375 milliseconds but gives the correct answer.