Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/18/84; site oddjob.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!oddjob!matt
From: matt@oddjob.UUCP (Matt Crawford)
Newsgroups: net.puzzle
Subject: Re: Find a set of positive real numbers whose sum is 100 and whose product is as large as possible.
Message-ID: <1167@oddjob.UUCP>
Date: Wed, 12-Feb-86 19:35:02 EST
Article-I.D.: oddjob.1167
Posted: Wed Feb 12 19:35:02 1986
Date-Received: Fri, 14-Feb-86 03:17:40 EST
References: <1057@decwrl.DEC.COM>
Reply-To: matt@oddjob.UUCP (Matt Crawford)
Organization: U. Chicago, Astronomy & Astrophysics
Lines: 21
Keywords: SPOILER

The subject line is long enough already!  Unless I forget, the
following will be a rot13 solution:

Snpg 1:  nyy ahzoref va gur frg ner rdhny.  Vs gurl jrera'g,
gura nal cnve bs hardhny ahzoref {n, o} va gur frg pbhyq or
ercynprq ol { (n+o)/2, (n+o)/2 } tvivat n ynetre cebqhpg jvgu
gur fnzr fhz.  (Jbex bhg gur znkvzvmngvba ceboyrz sbe n*o
fhowrpg gb n+o=p.  Lbh trg n=o.)

Gurersber, gur frg bs ahzoref (npghnyyl n "ont") jvyy or a
pbcvrf bs 100/a, sbe fbzr a.  Gerngvat a nf n pbagvabhf inevnoyr
naq znkvzvmvat (100/a)^a tvirf a=100/r ~= 36.79, fb gur nafjre
jvyy or a=36 be a=37.  Gelvat gurz obgu fubjf gung a=37 vf gur
nafjre naq gur cebqhpg vf nobhg 9.400r15.

The pure mathemetician will criticize some of the glib
shortcuts, but this is how a physicist solves it.  The answer is
right and it took only 4 minutes, so think before you flame!
_____________________________________________________
Matt		University	crawford@anl-mcs.arpa
Crawford	of Chicago	ihnp4!oddjob!matt