Problem 1

Problem 1: 

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

If you recall - natural numbers are simply positive whole numbers (no decimals!).So my first impression as to tackling this problem is to loop a number from 1 to 999 and divide by 3 and 5 along the way. Anything that divides with no remainder goes evenly into the number and should be added to a running total.


Ok, sounds easy enough. but i'll need to know what the syntax is for a for loop and an if statement.


For Loop syntax:
for (initial condition variable; condition is some circumstance; increment the original variable to progress through the loop). 


Lets look at an example and use the knowledge that we need to loop from 1 to 999


Example:

for (x = 1; x <= 999; x++)
    {

        do stuff here
    }

If Statement syntax:
if (variable <operator> equals result)
Example:

if(x%3 == 0)
     {
          do stuff
     }

Mod command:
Now the "%" symbol is called mod. The mod command returns the remainder of the division of x divided by 3. This is useful to us in this question to check if 3 or 5 goes evenly into x.

Or Command:
Double pipe "||" is the or statement in C#, we'll be using that to see if x%3 or x%5 is 0.

So my entire code solution for this problem is:

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

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int x = 1;
            int y = 0;
            for (x = 1; x < 1000; x++)
            {
                if (x % 3 == 0 || x % 5 == 0)
                    y = y + x;
            }
            Console.WriteLine("The Answer is: ");
            Console.WriteLine(y);
        }
    }
}

This seems to run pretty darn fast and outputs the correct statement. I've chosen to run a console application from the projects window and use Crtl + F5 to have the console window stay open after I run the code.

I will work on better code formatting in future posts but as you can see we're simply looping from 1 to 999 and dividing by 3 and 5 at each loop. If the remainder is zero we add it to our running total variable of "y".