### Project Euler

#### Problem 1: Multiples of 3 or 5

"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."

This problem was a good way to get back into the swing of things after a few months of not touching Java. I approached this by implementing a counter for loop which ensured that our range never exceeded 1000. Moreover, whenever the remainder of our counter variable equalled 0 when divided by one of our natural numbers (3 or 5), our if statement would distinguish it as a multiple and add it to our sum variable.

** Problem 2: Even Fibonacci Numbers **

"Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms."

I began this problem by establishing the rules surrounding the Fibonacci sequence -- (Fn = Fn − 1 + Fn − 2 in this instance: F0 = 1 & F1 = 2). This allowed me to declare the first two variables (a representing F0 and b representing F1). From here I decided to use a while loop as I was unsure how many terms we would end up with, however, also respected our maximum range of 4,000,000 by ensuring we exited the loop once variable a reached it. Furthermore, so that our sum was a culmination of only even numbers, I implemented an if statement that tested for this.