Problem 249. Project Euler: Problem 9, Pythagorean numbers

Created by Doug Hull

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A Pythagorean triplet is a set of three natural numbers, a b c, for which,

 a^2 + b^2 = c^2

For example,

 3^2 + 4^2 = 9 + 16 = 5^2 = 25.

There exists exactly one Pythagorean triplet for which a + b + c = N (the input).

Find the product abc.

Thank you to Project Euler Problem 9.

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Solution Stats

483 Solutions
170 Solvers

Last Solution submitted on Apr 04, 2020

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

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Aurelien Queffurust on 22 May 2012

The description should be 9 + 16 = 5^2 and not 9+16 = 2^5 ?

Ned Gulley on 22 May 2012

Thanks Aurelien! Fixed it.

Peter Wittenberg on 20 Dec 2012

This is an interesting problem. Apparently everyone (including me) had to solve it by a basic brute force method with oly very slight variations. I did manage to use my MATLAB copy to use solve from the symbolic toolbox to get the answers, but the version of MATLAB on which Cody runs doesn't have access to a license for the symbolic toolbox.

Srishti Saha on 13 Oct 2018

@ Doug Hall, I have solved all the problems in the series. However, I have not received the badge and the associated scores on completion of the series. Can you please help me with this?

Solution Comments

Solution 1605777

3 Comments

3 Comments

A C on 10 Aug 2018

It works, but this code takes too long. Can I reduce the code's time?

A C on 11 Aug 2018

lot1 = (floor(x/5));
lot2 = (floor(x/2.7):1:ceil(x/2.3));
lot = [lot1,lot2];

A C on 11 Aug 2018

prod([floor(x/5),ceil(x/2.6667),floor(x/2.35294)])

Solution 50788

3 Comments

3 Comments

Venu Lolla on 24 Feb 2012

Doug: Just wondering if the last test case is incorrect. It seems like for the input of 3200, the p-triplet should be (700, 1152, 1348) and y_correct should be 1087027200. Please do let me know if I am wrong. Cheers, VL.

Prateep Mukherjee on 27 Feb 2012

There is another one: (640,1200,1360). y_correct = 1044480000.

Doug Hull on 13 Mar 2012

I just noticed that. I had thrown in a new test suite because someone had hardcoded the solutions in. I guess I did not test it right. Problem solved and submissions are being rescored now.

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