X-Google-Language: ENGLISH,ASCII X-Google-Thread: f996b,ced2b975ce40b48d X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 2001-12-10 17:51:28 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news.ems.psu.edu!news3.cac.psu.edu!usenet From: William Newsgroups: alt.ascii-art Subject: Re: Tali's Moogies Date: Mon, 10 Dec 2001 20:50:41 -0500 Organization: Student, Penn State Univ. Lines: 51 Message-ID: <3C156670.A78DC80D@email.psu.edu> References: <3bf51490$0$765$edfadb0f@dspool01.news.tele.dk> <9t587n.3vvbkkh.1@MK.kasperhausen.de> <9tb7k0.3vvcs93.1@MK.kasperhausen.de> <3bf94951$0$25388$edfadb0f@dspool01.news.tele.dk> <3bf94a21.11777614@news.tpi.pl> <3bfa26a2.844203@News.CIS.DFN.DE> <3bfa5392.1511474@News.CIS.DFN.DE> <9tekel.3vvab97.1@MK.kasperhausen.de> NNTP-Posting-Host: tnt3-167-178.cac.psu.edu Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1; x-mac-type="54455854"; x-mac-creator="4D4F5353" Content-Transfer-Encoding: 8bit X-Mailer: Mozilla 4.75C-CCK-MCD {C-UDP; EBM-APPLE} (Macintosh; U; PPC) X-Accept-Language: en Xref: archiver1.google.com alt.ascii-art:12375 > I�m quite sure that I could do summing like this: > > +----------+----------+----------+----------+ > | | ___ | ___ | ___ | > | . | | . | | . | || . |___|| > | / \| | / \| | / \| | / \| | > | /___| | /___| | /___| | /___| | > | |\ /| | |\ /| | |\ /| | |\ /| | > | | X | | | X | | | X | | | X | | > | |/_\| | |/_\| | |/_\| | |/_\| | > | | | | | > +----------+----------+----------+----------+ > | mit�nem | Wimpel | oben | drauf | > +----------+----------+----------+----------+ > > This means that I had to end the Nikolaushouse at the upper left or right > corner. Now I tried all possible variations, but cannot do it again. Can > sumbuddy help? > > HJH > \ \ \ \ \ > \__\ \ \__\ > \ \ \ \ \ > \ \` _ / \ \ There are two kinds of nodes (places where lines cross, or start or end) - those with an even number of edges, and those with odd. If you think about the odd nodes, you'll notice that you must either start or stop at an odd node, since you can't "come in and leave" a whole number of times. If you could, there would be one edge for every entrance, and one edge for every leaving, making an even number of edges. So, since you must either start or stop at an odd node, you can't have any more than two in a single graph -- one to start at, one to stop at. Since the Nikolaushaus has its odd nodes at the lower corners (three edges each: a wall, the floor, and a diagonal), you must start and stop at those. So you can't start or stop at an upper corner -- and, like Mr. Rossel said, the picture you have is impossible anyway, since it has more than two odd nodes. William J. Keith -- math student, avid reader of a.a-a, first time poster (well, since one time a *long* time ago) Sample work: a turtle, swimming, I made for a friend of mine ___ ,+'/.\'+, ___ \/\_/\_/\_/\,+' * \ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ /_/'-------'\_\