Hey everyone,
I took a few weeks off posting in order to study for Exam MFE, which I took 4 weeks ago. I’m still waiting for the result, so in the meantime I’ve decided to knock out the CAS modules and finish up my SQL course before I have to start studying hard again. Anyway, I’ve finally gotten around to attempting the Project Euler problems that my friends, along with other actuaries, recommended to me as a good way to improve my programming skills.
Basically, Project Euler is a website that hosts mathematical problems that anyone can attempt to solve with whatever method they wish. Most of the problems are simply stated and can be understood by most people who have taken a basic course in number theory. However, they are often very computationally intensive if attempted directly so most people try to solve them by writing computer programs. Oftentimes students will use the site in an iterative fashion to practice their programming skills when picking up a new language. For example, one of my colleagues who has solved 80 problems first used the site to learn VBA, and then did the same problems again in R, and then again in C++.
For my first attempt, I decided to use VBA because I already know most of the basic syntax. Before starting, I decided that I would not seek any outside help or lookup any solutions when trying to solve these problems, because I want to work these out on my own. So please don’t give me any tips! (although I do appreciate any advice for any of my other projects).
The first problem is stated as follows:
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.
Solution:
[code language=”vb”]
Sub euler1()
Dim x As Long ‘natural number to be tested
Dim y As Long ‘current sum of the multiples of 5 or 3
y = 0
For x = 1 To 999
If x Mod 3 = 0 Or x Mod 5 = 0 Then
y = y + x
End If
Next x
Debug.Print y
End Sub
[/code]
The final output is 233168. As you can see, the problem is quite easy to understand (and this one was very easy to solve as well) for anyone who passed grade school math. You can probably solve it by sitting at your desk and adding every multiple of 3 or 5 below 1000 by hand, but that would be extremely boring and you probably have better things to do. That’s why you write a program to solve the problem. The solution I wrote above is a simple brute force method (I tested every natural number below 1000 to see if it was evenly divided by 3 or 5) that took less than a second for my computer to solve. The key to understanding the solution is the mod operator, which returns the remainder in a division operation (for example 5 mod 3 equals 2). The statement “If x Mod 3 = 0 Or x Mod 5 = 0” tells the computer to execute the subsequent line, or to add x to the cumulative sum if either x mod 3 or x mod 5 equals 0, in other words, if the remainder after dividing x by 3 or 5 is 0.
