Re: Inflight magazine puzzle

*To*: mathgroup at smc.vnet.net*Subject*: [mg50406] Re: Inflight magazine puzzle*From*: "Hans Michel" <hmichel at cox.net>*Date*: Thu, 2 Sep 2004 04:34:34 -0400 (EDT)*References*: <ch3orp$4a$1@smc.vnet.net>*Reply-to*: "Hans Michel" <hmichel at cox.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul: This looks like the quasigroup completion problem Go here: http://www.cs.cornell.edu/Info/People/gomes/QUASIdemo.html However this was done in Java. They use colours instead of numbers. I had some correspondence with Dr Gomes about this problems relation to Magic, Latin Squares, and Knights Tour over 4 years ago. But I took it no further. With the probable inclusion in Mathematica Journal could be incentive to put my hunch to the test. Hans "Paul Abbott" <paul at physics.uwa.edu.au> wrote in message news:ch3orp$4a$1 at smc.vnet.net... > The following puzzle appeared in an AirCanada inflight magazine. It's > not too hard to solve by hand, but I'd be interested to hear about > clever solutions using Mathematica. What would be particularly nice > would be to see an animation showing the steps (and possible > back-tracking) towards the unique solution. I'd like to include the best > solution(s) in an issue of The Mathematica Journal. > > Cheers, > Paul > > ________________________________________________________________________ > In the diagram below (copy the Cell[...] below and paste into a > Notebook, answering yes when it asks you if you want Mathematica to > interpret it), place the numbers 1 through 9 so that each row, column, > and 3 x 3 subsquare (separated by thick black lines) contains each > number exactly once. > > Cell[BoxData[FormBox[RowBox[{RowBox[{"puzzle", "=", > GridBox[{ > {" ", "3", " ", "9", " ", " ", " ", "8", " "}, > {" ", " ", "6", "2", " ", "3", "7", "9", " "}, > {" ", " ", " ", "1", " ", " ", " ", " ", " "}, > {" ", "2", " ", "3", " ", " ", " ", "7", " "}, > {" ", " ", " ", " ", "7", " ", " ", "6", "4"}, > {"1", " ", " ", " ", " ", " ", " ", " ", " "}, > {" ", "5", " ", " ", " ", "4", "9", " ", " "}, > {" ", "7", "2", " ", " ", " ", " ", " ", " "}, > {" ", "9", " ", " ", "5", " ", "8", "3", " "}}]}], ";"}], > StandardForm]], "Input", > GridBoxOptions->{ > GridFrame->True, > RowLines->{0.25, 0.25, True, 0.25, 0.25, True, 0.25}, > ColumnLines->{0.25, 0.25, True, 0.25, 0.25, True, 0.25} > } > ] > > -- > Paul Abbott Phone: +61 8 9380 2734 > School of Physics, M013 Fax: +61 8 9380 1014 > The University of Western Australia (CRICOS Provider No 00126G) > 35 Stirling Highway > Crawley WA 6009 mailto:paul at physics.uwa.edu.au > AUSTRALIA http://physics.uwa.edu.au/~paul >