## Monday, February 22, 2010

### Project Euler

My colleague from the computer science department at Contra Costa College, Tom Murphy, thought I might enjoy some more math problems, and pointed me to Project Euler. Here's their intro:
Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.
My programming skills are a bit rusty, so I'm starting with purely mathematical problems. The first one I did is:
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.
[I asked for the problems to be listed in ascending order of difficulty, and this one came up first.]

I figured it out, and used my calculator to do a simple multiplication and addition problem at the end. The 'forum' discussing this problem had lots and lots of programs listed. I was shocked people would ask a computer to solve this one.

I decided to do one a day. This morning I checked the next two and figured I'd at least want to use Excel on them, although I bet there's an elegant way to solve each of them without it. The fourth problem was once again simple enough to solve in a minute, with my trusty TI-83 doing my multiplication.

It looks like a nice set of problems to challenge students with. Thanks, Tom.

#### 6 comments:

1. Sue,
Thanks, I was just looking for some material to stimulate a couple of independent study students who are into (guess what) math and programming... sounds like my kind of source.

2. You're welcome, Pat. Glad I could return the favor in a small way. (You have given us all so many great resources...)

3. When you get to Euler problem 36, check out my article http://www.exploringbinary.com/finding-numbers-that-are-palindromic-in-multiple-bases/ (of course only after you try it yourself first.)

4. I've played with Project Euler for a long time. Lots of the problems take lots of thought, though.

5. Project Euler is amazing and I agree with you -- many of the problems can be solved without a fancy program in Python, C#, or whatever the flavor of the week is.

FWIW, A middle school computer programming class of mine solved about 20 Euler problems using little more than Excel. (I wrote about it at http://kalamitykat.com/2008/12/15/project-euler-math-programming-challenges/)

If you want less computer-y but a similar flavor, I liked _Thinking Mathematically_ by John Mason.

6. Hmm, i might have a copy of that book (but I haven't used it). The cover looks familiar.

Thanks for the mention. I'll look for it next time I'm at my office. (I'm on sabbatical for the year.)

I just did my 3rd problem. I had to use Excel on this one (sum of all the even Fibonacci numbers under 4 million), but it was way quick. I didn't even do a formula for even, since there were only about 10 numbers. I just copied them over to another column by hand, and summed.