NNTP-Posting-Date: Sun, 01 Jan 2012 22:04:47 -0600 Newsgroups: sci.logic,rec.puzzles,sci.math.num-analysis,comp.programming Date: Sun, 1 Jan 2012 20:04:45 -0800 From: William Elliot Subject: Re: the hourglass problem In-Reply-To: Message-ID: <20120101200139.B93055@agora.rdrop.com> References: <7f48dfe5-ca54-49ca-8cb9-5ae686e96f92@c42g2000prb.googlegroups.com> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed Lines: 27 X-Usenet-Provider: http://www.giganews.com NNTP-Posting-Host: 199.26.172.34 X-AuthenticatedUsername: NoAuthUser X-Trace: sv3-GbMD0ipmvb9nLjRTQ47tYptNAjoPtnGw4G8IS5Lk8Bj4y6Y5OsvPRcVKTfemHbj8LP8Zoi9rO0QWGZ8!aCvpWsssp5AgqNcRLcVd4/vJIFuwKvD2p4hfIuuKUJ/aJtaOrNKicfwC4PtdSNKrfWMrZeDaq0X3!zr0CX37+ X-Complaints-To: abuse@scnresearch.com X-DMCA-Complaints-To: abuse@scnresearch.com X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 X-Original-Bytes: 2135 Path: csiph.com!x330-a1.tempe.blueboxinc.net!usenet.pasdenom.info!news.stben.net!border3.nntp.ams.giganews.com!border1.nntp.ams.giganews.com!border4.nntp.ams.giganews.com!border2.nntp.ams.giganews.com!feeder2.cambriumusenet.nl!feeder1.cambriumusenet.nl!feed.tweaknews.nl!postnews.google.com!news1.google.com!border1.nntp.dca.giganews.com!nntp.giganews.com!local2.nntp.dca.giganews.com!nntp.scnresearch.com!news.scnresearch.com.POSTED!not-for-mail Xref: x330-a1.tempe.blueboxinc.net comp.programming:1179 On Sun, 1 Jan 2012, root wrote: > RichD wrote: >> You're given a 7 minute, and a 4 minute, sand >> hourglass. Measure a 9 minute interval, in the first >> 9 minutes. (no 'setup' period) >> >> ok, this is trivial. But as computer nerds, we're >> interested in general solutions. So, given hourglasses >> of n and m minutes: >> >> 1) Can you devise a formula which generates a list of >> all possible intervals produced by them? > This problem is very interesting. After you realize > how to get 9 minutes, you then realize you are > able to get 4 minutes, 7 minutes, and then every > integer minute thereafter. So the numbers realizable > without delay are: > 4,7,8,9,10,11,12........ > How did you realize 9, 10 and 11 without any delay? > Then, clearly, with a 7 minute delay you can generate > every integer minute. How can you generate 2 and 9 with only a 7 minute delay?