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Inflight magazine puzzle

• To: mathgroup at smc.vnet.net
• Subject: [mg50393] Inflight magazine puzzle
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 1 Sep 2004 01:49:43 -0400 (EDT)
• Organization: The University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Inflight magazine puzzle
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Inflight magazine puzzle
    • From: DrBob <drbob@bigfoot.com>