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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
>