(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1135607, 21046]*) (*NotebookOutlinePosition[ 1136314, 21071]*) (* CellTagsIndexPosition[ 1136270, 21067]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["New Knight's Tour.", FontSize->36]], "Subtitle"], Cell[TextData[{ StyleBox["Yuya Kakoi,Naoki Saida,Kazuki Takeshima,Yoshiaki Ohishi, Hiroshi \ Matsui,Toshiyuki Yamauchi, Takashi Kajimoto, Kanta Yoza, Akihiro Hyogu, Yuta \ Nakagawa, Naoyuki Totani and Ryohei Miyadera", FontSize->18, FontSlant->"Italic"], StyleBox["\nmiyadera1272000@yahoo.co.jp", FontSize->16] }], "Text", FontFamily->"Courier New"], 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", FontFamily->"Courier New"], "If the final position is a knight's move away from the first position, we \ call the tour re-entrant. ", StyleBox["The tour that is re-entrant is a Hamiltonian circuit.", FontFamily->"Courier New"] }], "Text", FontFamily->"Courier New", FontSize->16], Cell[TextData[{ StyleBox["Remark.", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" This kind of graphs are already studied for the traditional \ Knight's Tour. Please look for Knight's Tour in ", FontFamily->"Courier New"], StyleBox["MathWorld", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[".", FontFamily->"Courier New"] }], "Text", FontFamily->"Courier New", FontSize->16], Cell[BoxData[ \(\(\(http\)\(:\)\) // mathworld . wolfram . com/KnightsTourGraph . html\)], "Input"], Cell[TextData[{ StyleBox["You can find beautiful graphs that the authors made in MathArt ", FontFamily->"Courier New"], StyleBox["published by the Mathematical Institute, Belgrade, Yugoslavia", FontFamily->"Courier"], StyleBox[". ", FontFamily->"Times"] }], "Text", FontFamily->"Courier New", FontSize->16], Cell[BoxData[ \(\(\(http\)\(:\)\) // \(\(www . mi . sanu . ac . yu/vismath\)/ miyadera2007knight\)/graph . html\)], "Input"], Cell[TextData[{ StyleBox["W", FontFamily->"Courier New"], StyleBox["e are the first people who began to look for variants of Knight's \ tour that present us beautiful graphs.", FontFamily->"Courier New"] }], "Text", FontFamily->"Courier New", FontSize->16], Cell[TextData[{ StyleBox["How we can make board, boardnumbers and the graph using ", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox["Mathematica", FontFamily->"Courier New", FontWeight->"Bold", FontSlant->"Italic"], StyleBox[".", FontFamily->"Courier New", FontWeight->"Bold"], StyleBox[" ", FontFamily->"Courier New"] }], "Text", FontFamily->"Courier New", FontSize->16], Cell[TextData[StyleBox["Once you make a variant of knight's tour by using a \ paper and a pencil, then you can represent the solution of the problem as a \ matrix.", FontFamily->"Courier New"]], "Text", FontFamily->"Courier New", FontSize->16], Cell[TextData[StyleBox["For example the above problem can be represented by \ the following matrix.", FontFamily->"Courier New"]], "Text", FontFamily->"Courier New", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{"ohishi", "=", RowBox[{"(", GridBox[{ {"0", "0", "23", "0", "0", "0", "21", "0", "0"}, {"0", "0", "0", "19", "22", "17", "0", "0", "0"}, {"29", "0", "0", "24", "0", "20", "0", "0", "15"}, {"0", "25", "28", "0", "18", "0", "16", "11", "0"}, {"0", "30", "0", "26", "0", "10", "0", "14", "0"}, {"0", "27", "32", "0", "6", "0", "12", "9", "0"}, {"31", "0", "0", "4", "0", "8", "0", "0", "13"}, {"0", "0", "0", "7", "2", "5", "0", "0", "0"}, {"0", "0", "3", "0", "0", "0", "1", "0", "0"} }], ")"}]}], ";"}]], "Input", FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(<<\)\(DiscreteMath`Combinatorica`\)\( (*It\ is\ essential\ to\ load\ \ this\ package\ before\ you\ use\ the\ 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