From john_bailey@rochester.rr.com Wed Mar 31 16:12:25 CST 2004 Article: 286224 of sci.math Path: news!news.niu.edu!news.illinois.net!newsfeed2.dallas1.level3.net!news.level3.com!zeus.visi.com!news-out.visi.com!green.octanews.net!news-out.octanews.net!news.glorb.com!border1.nntp.ash.giganews.com!nntp.giganews.com!news.maxwell.syr.edu!news-rtr.nyroc.rr.com!news-out.nyroc.rr.com!twister.nyroc.rr.com.POSTED!53ab2750!not-for-mail From: john_bailey@rochester.rr.com (John Bailey) Newsgroups: sci.math Subject: Re: Inverse Problems and Games Message-ID: <406abaf6.127938835@news-server.rochester.rr.com> References: X-Newsreader: Forte Free Agent 1.11/32.235 Lines: 40 Date: Wed, 31 Mar 2004 12:45:56 GMT NNTP-Posting-Host: 66.67.126.162 X-Complaints-To: abuse@rr.com X-Trace: twister.nyroc.rr.com 1080737156 66.67.126.162 (Wed, 31 Mar 2004 07:45:56 EST) NNTP-Posting-Date: Wed, 31 Mar 2004 07:45:56 EST Organization: Road Runner Xref: news sci.math:286224 On Wed, 31 Mar 2004 12:07:39 GMT, Tim Brauch wrote: >I am looking for "scholarly" resources that look at games as inverse >problems. For example, Mastermind (I think it is also called Mindbreaker) >is supposed to be an inverse combinatorial problem. I am sure there are >others, and even resources about games and game theory as an inverse >problem, but I am having trouble finding things. > Does "lights out" qualify? http://www.haar.clara.co.uk/Lights/ http://www.hamusutaa.com/pilot/solution.html (quoting) There are 225, or 33,554,432 different possible combinations of lights on the Lights Out board. By no coincidence, if you were to try and solve a puzzle through brute force, there are 33,554,432 different possible solutions you would need to try. (end quote) also: From: Carsten Haese Subject: Mathematical Puzzle: Turn all the lights out Date: 1998/02/12 Message-ID: Organization: Technical University Berlin, Germany Newsgroups: sci.math Abstract -------- This paper is concerned with a mathematical solution of an electronic puzzle game called "Lights Out". "Lights Out" is a commercially available product, so to protect myself I expressly state that this paper is not intended to influence you in any way to buy or not to buy "Lights Out". My only intention is to present a result of entertaining mathematical research and to share it with anyone who is interested in it. (snip) John Bailey http://home.rochester.rr.com/jbxroads/mailto.html From john_bailey@rochester.rr.com Wed Mar 31 16:12:44 CST 2004 Article: 286251 of sci.math Path: news!news.niu.edu!news.illinois.net!newsfeed2.dallas1.level3.net!news.level3.com!zeus.visi.com!priapus.visi.com!orange.octanews.net!news-out.visi.com!hermes.visi.com!news.octanews.net!feed2.news.rcn.net!rcn!border1.nntp.ash.giganews.com!nntp.giganews.com!news.maxwell.syr.edu!news-rtr.nyroc.rr.com!news-out.nyroc.rr.com!twister.nyroc.rr.com.POSTED!53ab2750!not-for-mail From: john_bailey@rochester.rr.com (John Bailey) Newsgroups: sci.math Subject: Re: Inverse Problems and Games Message-ID: <406ad111.133599013@news-server.rochester.rr.com> References: X-Newsreader: Forte Free Agent 1.11/32.235 Lines: 63 Date: Wed, 31 Mar 2004 14:43:25 GMT NNTP-Posting-Host: 66.67.126.162 X-Complaints-To: abuse@rr.com X-Trace: twister.nyroc.rr.com 1080744205 66.67.126.162 (Wed, 31 Mar 2004 09:43:25 EST) NNTP-Posting-Date: Wed, 31 Mar 2004 09:43:25 EST Organization: Road Runner Xref: news sci.math:286251 On Wed, 31 Mar 2004 12:07:39 GMT, Tim Brauch wrote: >I am looking for "scholarly" resources that look at games as inverse >problems. For example, Mastermind (I think it is also called Mindbreaker) >is supposed to be an inverse combinatorial problem. I am sure there are >others, and even resources about games and game theory as an inverse >problem, but I am having trouble finding things. Does the Nokkia rotation game qualify? Realizing you were asking for scholarly references, I did a search using the site criteria: site:edu and checked the resulting articles reference lists. Here is a sampling of those results for both rotation and lights out games: http://www.users.muohio.edu/porterbm/sumj/2001/Beal.pdf http://web.usna.navy.mil/~wdj/book/node157.html http://www.mailcom.com/NokiaRotation.html http://www.press.jhu.edu/books/title_pages/3288.html 1. Anderson, Marlow and Feil, Todd, Turning Lights Out with Linear Algebra, Math Magazine (4) 71 (1998), 300–303. http://www.psc.edu/~burkardt/puzzles/lights_out_solution.html References: Alexander Shen, Mathematical Entertainments: Lights Out, Mathematical Intelligencer, Volume 22, Number 13, Summer 2000, pages 20-21. (a cryptic and hurried discussion) Marlow Anderson and Todd Feil, Turning Lights Out with Linear Algebra, Mathematics Magazine, Volume 71, Number 4, October 1998, pages 300-303. (discusses general initial configuration, larger boards, and problems on a torus) Oscar Martin-Sanches and Cristobal Pareja-Flores have a web site containing a very nice Visual Basic implementation of the puzzle. (Although they supply a standalone executable, I could not get it to work until I went out and bought my own copy of Visual Basic. Happy Birthday, Bill!) Uri Peled, Problem 10197, American Mathematical Monthly, Volume 99, Number 2, February 1992, page 162. O P Lossers, An All-Ones Problem A Solution to Problem 10197, American Mathematical Monthly, Volume 100, Number 8, October 1993, pages 806-807. F Galvin, Solution to Problem 88-8, Mathematical Intelligencer, Volume 11, Number 2, 1989, pages 31-32. K Sutner, Linear Cellular Automata and the Garden-of-Eden, Mathematical Intelligencer, Volume 11, Number 2, 1989, pages 49-53. John Bailey http://home.rochester.rr.com/jbxroads/mailto.html