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YMBMO: Project Euler

By - Posted on 28 August 2010

Do you like puzzles? Many do! Do you like programming? Not as many people do! Do you like programming puzzles? If you’re in the intersection of the Venn diagrams of “Puzzle lover” and “Programming lover,” then this article is for you! This week in YMBMO, enter Project Euler!

What is Project Euler?

Project Euler is a site that features a variety of mathematical problems that you are supposed to solve using your ingenuity, reasoning and programming skills. Problems range from as simple as problem 1:

"Add all the natural numbers below one thousand that are multiples of 3 or 5."

To as complex as Problem 263:

"Consider the number 6. The divisors of 6 are: 1,2,3 and 6.
Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:
1=1, 2=2, 3=1+2, 4=1+3, 5=2+3, 6=6.
A number n is called a practical number if every number from 1 up to and including n can be expressed as a sum of distinct divisors of n.
A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).
We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.
We shall call a number n such that :
•   (n-9, n-3), (n-3,n+3), (n+3, n+9) form a triple-pair, and
•   the numbers n-8, n-4, n, n+4 and n+8 are all practical,
Find the sum of the first four engineers’ paradises.
"

And that isn’t the hardest… or even the sexiest.

Who was Euler?

Ever heard of e? Well, that shit is Euler’s number! Just like pieces are Reese's!

Hands off, bitches!

Euler’s identity is considered by some to be the most beautiful thing they’ve ever seen, because it combines 5 fundamental mathematical constants: 0, 1, pi, e and i.

It’s also available on a wide array of t-shirts.

And teeth.

Where should I start?

At the beginning. The first problem is the easiest. You can list the problems in order of ascending difficulty to solve all the less involved problems first.

At the problem list page you can also see how many people have solved the problem, and use that as a an estimate of difficulty. As explained on the sites "About" section, if you write a proper program any problem should be able to be computed in about one minute. That is, one minute from the time you execute your program. Writing the program in the first place is the difficult bit…

LOL GET IT?! BIT.... COMPUTER.... HAHAHAH
...No? .... My comedy stylings are wasted on you philistines.

When do I have to finish all the problems by?

Woah, there cowboy! Some of these problems are serious business. Don’t feel like you’re in a rush to complete every problem on the site. Just enjoy a fine sampling.

Then again, every 25 problems you solve will gain you higher rankings.

Hell yeah!

Why should I do this?

Because it’s fun! Besides, it will help keep your problem solving, mathematical and programming skills sharp!