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        riddles >> medium >> 271
        
(Message started by: tereferekuku on Sep 21^st, 2009, 12:27pm)

Title: 271
Post by tereferekuku on Sep 21^st, 2009, 12:27pm

"Write 271 as the sum of positive real numbers so as to maximize their product."

SOLUTION:
e^99*e^(271/e-99)

Title: Re: 271
Post by towr on Sep 21^st, 2009, 1:29pm

I don't see any + sign, or a http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gif. So at the very least you haven't written 271 as the sum of anything.
And e^99 + e^(271/e-99) isn't 271 either; it's rather a long way off.

Title: Re: 271
Post by tereferekuku on Sep 21^st, 2009, 3:21pm

OK, sum_1^99{e} + e^{271/e-99}. Is that better?

Title: Re: 271
Post by BenVitale on Sep 21^st, 2009, 3:35pm

I worked on this problem just few days ago.

See Here (http://qbyte.org/puzzles/p008s.html)

Title: Re: 271
Post by towr on Sep 22^nd, 2009, 1:45am

on 09/21/09 at 15:21:58, tereferekuku wrote:

OK, sum_1^99{e} + e^{271/e-99}. Is that better?

It's about 271.114269, though; not 271. But it's very close to the solution Ben linked to.

Title: Re: 271
Post by tereferekuku on Sep 22^nd, 2009, 3:21am

Yes, of course, I meant sum_1^99{e} + e*{271/e-99}, which adds up just fine to 271, but the issue I forgot about is that ALL factors should be equal in order to maximize the product, hence Ben's solution is still slightly bigger than mine.

Title: Re: 271
Post by R on Sep 23^rd, 2009, 9:11pm

What is so special about 271?

Title: Re: 271
Post by BenVitale on Sep 23^rd, 2009, 10:06pm

Consider, for example, 271 is the smallest prime p such that (p - 1) and (p + 1) are each divisible by a cube greater than one.

http://primes.utm.edu/curios/page.php/271.html

Title: Re: 271
Post by towr on Sep 24^th, 2009, 12:21am

on 09/23/09 at 21:11:35, R wrote:

What is so special about 271?

In this case? It's the second closest integer to 100*e

Title: Re: 271
Post by R on Sep 24^th, 2009, 12:57am

on 09/23/09 at 22:06:49, BenVitale wrote:

Consider, for example, 271 is the smallest prime p such that (p - 1) and (p + 1) are each divisible by a cube greater than one.

http://primes.utm.edu/curios/page.php/271.html

lol ;D
Maths have a story behind every number. :P