From dan@math.uiuc.edu Sat Jul 29 20:41:28 2000 Received: from alpha.math.uiuc.edu (alpha.math.uiuc.edu [128.174.110.100]) by mail.math.niu.edu (8.9.1a/8.9.1) with ESMTP id UAA03925 for ; Sat, 29 Jul 2000 20:41:27 -0500 (CDT) Received: from orion.math.uiuc.edu (orion.math.uiuc.edu [128.174.111.4]) by alpha.math.uiuc.edu (8.9.3/8.9.3) with ESMTP id UAA12285 for ; Sat, 29 Jul 2000 20:41:28 -0500 (CDT) Received: (from dan@localhost) by orion.math.uiuc.edu (8.9.1b+Sun/8.9.0) id UAA07739; Sat, 29 Jul 2000 20:41:27 -0500 (CDT) Date: Sat, 29 Jul 2000 20:41:27 -0500 (CDT) Message-Id: <200007300141.UAA07739@orion.math.uiuc.edu> X-Authentication-Warning: orion.math.uiuc.edu: dan set sender to dan@math.uiuc.edu using -f From: "Daniel R. Grayson" To: David Rusin Subject: games Reply-to: dan@math.uiuc.edu Status: R Have you ever analyzed the electronic solitaire game, "Lights Out"? From rusin@math.niu.edu Sun Jul 30 03:03:18 2000 Received: from vesuvius.math.niu.edu (vesuvius.math.niu.edu [131.156.3.93]) by mail.math.niu.edu (8.9.1a/8.9.1) with ESMTP id DAA04358; Sun, 30 Jul 2000 03:03:17 -0500 (CDT) From: Dave Rusin Received: (from rusin@localhost) by vesuvius.math.niu.edu (8.9.3/8.8.5) id DAA24726; Sun, 30 Jul 2000 03:03:17 -0500 (CDT) Date: Sun, 30 Jul 2000 03:03:17 -0500 (CDT) Message-Id: <200007300803.DAA24726@vesuvius.math.niu.edu> To: dan@math.uiuc.edu Subject: Re: games Cc: rusin@math.niu.edu Status: R I've never actually played Lights Out but I have had some people ask me about it. THere are several threads of conversation about it at http://www.math.niu.edu/~rusin/papers/uses-math/games/other/lights Note that at the end of the file is a message from someone else telling me they had written a little paper about it. (There are some URLs there too if you want to see more.) It's a question of writing elements of the vector space ( GF(2) )^25 in terms of a specific basis. As I recall the question is not all that interesting as given but the generalizations to other dimensions and to the corresponding integral question are not so clear to me. I've lost track of the summer smr rotation but on the assumption that we're back to normal now I'll be checking my mailbox starting next week for posts to moderate. dave From dan@math.uiuc.edu Sun Jul 30 07:18:59 2000 Received: from alpha.math.uiuc.edu (alpha.math.uiuc.edu [128.174.110.100]) by mail.math.niu.edu (8.9.1a/8.9.1) with ESMTP id HAA04622 for ; Sun, 30 Jul 2000 07:18:59 -0500 (CDT) Received: from orion.math.uiuc.edu (orion.math.uiuc.edu [128.174.111.4]) by alpha.math.uiuc.edu (8.9.3/8.9.3) with ESMTP id HAA20172 for ; Sun, 30 Jul 2000 07:18:59 -0500 (CDT) Received: (from dan@localhost) by orion.math.uiuc.edu (8.9.1b+Sun/8.9.0) id HAA08624; Sun, 30 Jul 2000 07:18:59 -0500 (CDT) Date: Sun, 30 Jul 2000 07:18:59 -0500 (CDT) Message-Id: <200007301218.HAA08624@orion.math.uiuc.edu> X-Authentication-Warning: orion.math.uiuc.edu: dan set sender to dan@math.uiuc.edu using -f From: "Daniel R. Grayson" To: rusin@math.niu.edu In-reply-to: <200007300803.DAA24726@vesuvius.math.niu.edu> (message from Dave Rusin on Sun, 30 Jul 2000 03:03:17 -0500 (CDT)) Subject: Re: games Reply-to: dan@math.uiuc.edu References: <200007300803.DAA24726@vesuvius.math.niu.edu> Status: R Thanks for the link - the solution there by Carsten Haese is not accessible to a human, since he uses a computer to invert a 25x25 matrix. I've used the game as a teaching device in my linear algebra class twice. We start with the Super Lights Out game, because all the positions are solvable. The wonderful thing is that initial attempts to win by turning off all the lights except those in the bottom row can be explained as in terms of elementary column operations, and we use them to develop the standard algorithm for finding a basis for the span of any set of vectors, and after that, the algorithm for telling whether a vector is in the span. It seems more fun than the traditional approach where we start with the solution set of a system of equations, and learn about *row* operations first. As for the Super Lights Out game, the computation of the winning algorithm can be done completely by hand. ----------------------------------------------------------------------------- From: Dave Rusin Date: Sun, 30 Jul 2000 03:03:17 -0500 (CDT) Cc: rusin@math.niu.edu I've never actually played Lights Out but I have had some people ask me about it. THere are several threads of conversation about it at http://www.math.niu.edu/~rusin/papers/uses-math/games/other/lights Note that at the end of the file is a message from someone else telling me they had written a little paper about it. (There are some URLs there too if you want to see more.) It's a question of writing elements of the vector space ( GF(2) )^25 in terms of a specific basis. As I recall the question is not all that interesting as given but the generalizations to other dimensions and to the corresponding integral question are not so clear to me. I've lost track of the summer smr rotation but on the assumption that we're back to normal now I'll be checking my mailbox starting next week for posts to moderate. dave From rjc@maths.ex.ac.uk Thu Mar 21 19:06:47 CST 2002 Article: 123005 of sci.math Path: news!husk.cso.niu.edu!vixen.cso.uiuc.edu!news.uchicago.edu!newsswitch.lcs.mit.edu!newspump.monmouth.com!newspeer.monmouth.com!uvsq.fr!freenix!fr.usenet-edu.net!usenet-edu.net!news.mailgate.org!mygate.mailgate.org!oregano.ulcc.wwwcache.ja.net!not-for-mail From: "Robin Chapman" Newsgroups: sci.math Subject: Re: puzzle Date: Mon, 18 Mar 2002 16:05:33 +0000 (UTC) Organization: Mailgate.ORG Server - http://www.Mailgate.ORG Lines: 24 Message-ID: <9bf27f313aa9efa737a89a230c00f5e0.22128@mygate.mailgate.org> References: NNTP-Posting-Host: oregano.ulcc.wwwcache.ja.net Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: news.mailgate.org 1016467309 11720 194.82.103.36 (Mon Mar 18 17:05:33 2002) X-Complaints-To: abuse@mailgate.org NNTP-Posting-Date: Mon, 18 Mar 2002 16:05:33 +0000 (UTC) Injector-Info: news.mailgate.org; posting-host=oregano.ulcc.wwwcache.ja.net; posting-account=22128; posting-date=1016467309 User-Agent: Mailgate Web Server X-URL: http://mygate.mailgate.org/mynews/sci/sci.math/9bf27f313aa9efa737a89a230c00f5e0.22128%40mygate.mailgate.org Xref: news sci.math:123005 Status: RO Content-Length: 444 "stephen" wrote in message news:bba58aa.0203180737.5263a776@posting.google.com... > can anyone solve this puzzle? > > http://www.mathsyear2000.co.uk/ > > go to GAMES > got FIVER See H. Eriksson, K. Eriksson and J. Sjostrand, Note on the lamp lighting problem available at http://www.ima.mdh.se/personal/keo/Forskning/preprints.htm Robin Chapman -- Posted via Mailgate.ORG Server - http://www.Mailgate.ORG