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?"
"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?"
ReplyDeleteIs it 232792560? This is divisible by all the numbers and I think its the smallest but not certain!
Ask Euler! At the Project Euler site. ;-) Join the game.
ReplyDeleteI 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.
ReplyDeleteI 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
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