tag:blogger.com,1999:blog-981719720100236931.post8597615203223068050..comments2023-03-24T09:38:57.165+00:00Comments on Racing Entropy: Project Euler, Problems 34 and 39NathanRyderhttp://www.blogger.com/profile/17963023116440525852noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-981719720100236931.post-67426261403351280412011-03-02T09:07:59.717+00:002011-03-02T09:07:59.717+00:00Hi Rudy,
Thanks for your question: it really made...Hi Rudy,<br /><br />Thanks for your question: it really made me think as I don't know where my notes are from when I did that! :)<br /><br />But here it is, proof by contradiction.<br /><br />For Pythagorean triple, we have a < b 2p/3. But that means that at least one of a,b is greater than p/3. So either a > c or b > c. But from our earlier starting point, a < b <c. So contradiction, and p/3 < c.<br /><br />Hope that helps! Actually, I'm struggling to remember why c < p/2, although I know there is a really good reason it is escaping me at the moment.<br /><br />NathanNathanRyderhttps://www.blogger.com/profile/17963023116440525852noreply@blogger.comtag:blogger.com,1999:blog-981719720100236931.post-53349560001692943772011-03-01T19:46:24.836+00:002011-03-01T19:46:24.836+00:00I looked at your solution for problem 39 and I is ...I looked at your solution for problem 39 and I is asked myself: Why is p/3 < c? Can you explain that?<br /><br />Thanks.<br /><br />Rudy MeijerRudy Meijerhttps://www.blogger.com/profile/01115388886931476083noreply@blogger.comtag:blogger.com,1999:blog-981719720100236931.post-2248521705391877382009-03-01T19:08:00.000+00:002009-03-01T19:08:00.000+00:00I've done one more this afternoon, had a go at ano...I've done one more this afternoon, had a go at another one - but which didn't work, so will have to have a think about how I approach it... Have two more lined up which I think I have the maths and skills to solve. One more which I know how to solve - except the numbers are too big for the regular integer class to handle!<BR/><BR/>Will blog about the one I've done when I have one more to talk about. Hoping to have completed my personal goal of 25 within 10 days at most... Aiming for by the end of this week! :)NathanRyderhttps://www.blogger.com/profile/17963023116440525852noreply@blogger.comtag:blogger.com,1999:blog-981719720100236931.post-48458140342178169572009-03-01T18:01:00.000+00:002009-03-01T18:01:00.000+00:00go go go!go go go!Unknownhttps://www.blogger.com/profile/17584157512006175174noreply@blogger.com