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Sunday, July 10, 2011

Project Euler - Revisited

In order of difficulty I have now solved the first 12 least difficult problems, of the 300+ total problems. I am still in the zone of the not so difficult stuff because I haven't reached a level yet.

A Pythagorean triplet is a set of three natural numbers, $a, b, c$, for which, $a^2 + b^2 = c2$ For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

Project Euler - Problem 9. This problem has been solved by 75913 people, ( problem 1 by 159750 people ).

When you have solved a problem you get access to the answer book. It then becomes clear what a difference it makes if you are somewhat literate in a tool like Mathematica. I have solved most problems so far, if not all. with one line of functional Mathematica code while the model answer is a three or four page pdf full of procedural code. - For a while I had the feeling I was cheating by using Mathematica, but the goal is clear. Solve. no matter what. I am not sure but I think Euler is mainly geared for computer geeks, although the problems so far could have been solved by intelligent programming alone, knowledge of mathematics makes a difference. Take this problem for example.

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Project Euler - Problem 5.

Solved this one without using my computer, thus simple. Because I have done an introductory course in Number Theory of course. Maybe it is not so simple otherwise, I don't think so actually.

If you are ever enjoying leisure time on Sudoku's, Euler is worth considering. More fun!

P.S.
Watched the movie Source code yesterday. Liked it so much that I will give Proof ( Jake Gyllenhaal has a part in it ) a second chance. Proof is not an action movie, it is more in the line of A Beautiful Mind. An attempt to answer "Where does genius end before it turns into undeniable insanity?"

1. "2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?"

Is it 232792560? This is divisible by all the numbers and I think its the smallest but not certain!

2. Ask Euler! At the Project Euler site. ;-) Join the game.

3. I didn't even know project Euler existed until reading this post. I've been looking for something exactly like this for the longest time. so thank you.

4. I had no idea Project Euler existed until reading this post. I've been looking for something exactly like this for the longest time. So, thank you. lol

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)