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Article #2749Re: Rubik's tour.
From: John Bailey
Date: Sat, 22 Jan 2000 00:00
Date: Sat, 22 Jan 2000 00:00
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2388 bytes
On Fri, 21 Jan 2000 23:39:24 GMT, "Androcles" <androcles@home.com> wrote: >There is a well-known little puzzle known as the "Knight's Tour". >The object of the puzzle is to have the (chess) knight visit all 64 squares >on the chessboard (snip) >Suppose we have Rubik's cube, and suggest a tour such that all possible >outcomes of the various configurations are presented. We begin with the >identity. >Question three, analogous to the knight's tour. >How many configurations are there, each to be visited once and once only? >Question four. >Is this possible? >Question five: >How many moves does it take to return to the identity? There may be other ways to interpret *tour* in the context of a Rubik cube but this one is a lot of fun. Using a Rubiks cube simulator with macro capability such as http://www.mud.ca/cube/cube.html enter a sequence of moves. How many repetitions of these identical moves will return the cube to its original state? What sequence requires the most repetitions to restore? John
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: fa70b,cb2f33b9a8d8dd55 X-Google-Attributes: gidfa70b,public X-Google-Thread: 10b299,cb2f33b9a8d8dd55 X-Google-Attributes: gid10b299,public X-Google-Thread: 109d8a,cb2f33b9a8d8dd55 X-Google-Attributes: gid109d8a,public X-Google-Thread: 102524,cb2f33b9a8d8dd55 X-Google-Attributes: gid102524,public X-Google-Thread: 1130d6,cb2f33b9a8d8dd55 X-Google-Attributes: gid1130d6,public X-Google-Thread: fc333,cb2f33b9a8d8dd55 X-Google-Attributes: gidfc333,public X-Google-Thread: fee76,cb2f33b9a8d8dd55 X-Google-Attributes: gidfee76,public From: jmb184@frontiernet.net (John Bailey) Subject: Re: Rubik's tour. Date: 2000/01/22 Message-ID: <3889ab01.487646@news.frontiernet.net> X-Deja-AN: 576121541 References: <387DD6C1.24CC@ameritech.net> <xuMh4.3648$j63.455581@news1.rdc2.pa.home.com> <3887BFD4.116B@ameritech.net> <NMSh4.3936$j63.485453@news1.rdc2.pa.home.com> <38884C17.50BD@ameritech.net> <M66i4.4432$j63.528634@news1.rdc2.pa.home.com> X-Complaints-To: abuse@frontiernet.net X-Trace: node17.cwnet.frontiernet.net 948546997 44890 209.130.218.21 (22 Jan 2000 13:16:37 GMT) Organization: Frontier GlobalCenter Inc. NNTP-Posting-Date: 22 Jan 2000 13:16:37 GMT Newsgroups: rec.puzzles,alt.math,sci.math,alt.math.recreational,alt.brain.teasers,misc.writing,cz.soc.mensa