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This is also known as the Knight's Tour. A Knight's tour is a seque nce of moves by a knight chess piece, which may only make moves that s imultaneously shift one square along one axis and two along the other \+ forming an L shape, such that each square of the board is visited exac tly once. This is also a way in which we explore the Hamiltonian path. 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::::::hEi]ymy;:::::::q?Zy=:::::::XAq_ymy;:::::::i=Zy=:::::::L>ry:::::: ::^Bjy;:::::::BKZy=:::::::J\\:yA:::::::::Z>;xI::::::::Cry ::::::::^Bjy;:::::::q_qkysy:::::::Zu::ry:::::::Zq;jy;:::::::Cry::::::::^Bjy;:::::::BKZ y=:::::::hEi]ymy;:::::::q?Zy=:::::::XAq_ymy;:::::::::BKZy=:::::::hEi]y my;:::::::q?Zy=:::::::XAq_ymy;:::::::i=Zy=:::::::L>ry::::::::^Bjy;:::: :::BKZy=:::::::J\\:yA:::::::::Z>;xI::::::::Cry::::::::^Bj y;:::::::q_qkysy:::::::Zu:K\\ lJ\\BK:::::::ZZJSD=^B:::::::jC:C<:::::::ZM:L>::::::::a:^B::::::::H;BK: ::::::ZlJJ>^>K\\::::::::_;Z>;:::::::<:::::::bFZ> K\\::::::::_;Z>;:::::::<<_[>K\\::::::::;;Z>;:::::::H;BK::::::::VZ>;:::::::JJryvY::::::::::::::::::a:^B::::::::H;BK::::: :::V:::::::bF:^B:::::::JJbF^BL>:::::::BB:^B:::::::jC bu>:AB:;J::::nc;ocC?:<::3:" }}{PARA 264 "" 0 "" {TEXT 268 0 "" }}} {EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 29 "with(networks): with(linalg):" }}{PARA 272 "" 1 "" {TEXT -1 57 "Warning, the names charpoly and rank have been redefin ed\n" }}{PARA 272 "" 1 "" {TEXT -1 80 "Warning, the protected names no rm and trace have been redefined and unprotected\n" }}}{SECT 0 {PARA 268 "" 0 "" {TEXT 269 40 "The Initial Purpose of the Knight's Tour" }} {PARA 264 "" 0 "" {TEXT -1 236 "In this section, I am hoping to accomp lish the initial stage of developing a chessboard and hopefuly get som e of the knight moving procedures to work. Most importantly get Maple to produce all the possible moves that a knight can move." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 7 "new(G):" }}}{EXCHG {PARA 264 "" 0 "" {TEXT 270 0 "" }{TEXT 264 191 "W ith the new graph G. I want to create a board with an nxn vertices us ing the following procedure called \"board\". The purpose of this pro cedure is to give the general nxn board of vertices." }}{PARA 264 "" 0 "" {TEXT 271 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 220 "By assig ning an initial size value I don't have to keep on changing the values within my procedures later in the program. I can just change the Siz e value here and then reproducing a new set of board and possible move s." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 290 8 "WARNING:" }{TEXT -1 135 " DO NOT assign a big number for \"Size > 5 \", unless you have the time to sit and wait..........for a really rea lllllllllllly long time." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 8 "Size:=5;" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#>%%SizeG\"\"&" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 197 "b oard := proc(n): for i from 1 to n \n do for j from 1 to n \n do addvertex([[i,j]],G): \n \+ od; \n od; \n end proc;" }} {PARA 272 "" 1 "" {TEXT -1 63 "Warning, `i` is implicitly declared loc al to procedure `board`\n" }}{PARA 272 "" 1 "" {TEXT -1 63 "Warning, ` j` is implicitly declared local to procedure `board`\n" }}{PARA 269 " " 1 "" {XPPMATH 20 "6#>%&boardGf*6#%\"nG6$%\"iG%\"jG6\"F+?(8$\"\"\"F.9 $%%trueG?(8%F.F.F/F0-%*addvertexG6$7#7$F-F2%\"GGF+F+F+" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 12 "board(Size);" }}{PARA 264 "" 0 " " {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 272 116 "By assigning a Siz e to this procedure we can have all the vertices stored in the graph G with a Size-by-Size table." }}{PARA 264 "" 0 "" {TEXT 273 0 "" }} {PARA 269 "" 1 "" {XPPMATH 20 "6#7$\"\"&F$" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 12 "vertices(G);" }}{PARA 270 "" 1 "" {XPPMATH 20 "6 #<;7$\"\"\"\"\"$7$F&F%7$\"\"#\"\"&7$F%F)7$F)\"\"%7$F)F&7$F%F*7$F%F%7$F %F-7$F-F-7$F-F&7$F-F)7$F-F%7$F&F*7$F&F-7$F&F&7$F&F)7$F*F*7$F*F-7$F*F&7 $F*F)7$F*F%7$F-F*7$F)F%7$F)F)" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 274 322 "The following procedure is to fi gure out the possible moves that a knight can move within an nxn board by assigning a vertex [i,j] to the procedure. Since the knight is mo ving in an [i+1,j+2], [i+1,j-2], [i-1,j+2], [i-1,j-2], [i+2,j+1], [i+2 ,j-1], [i-2,j+1], or [i-2,j-1] position, the procedure can be written \+ as follow." }}{PARA 264 "" 0 "" {TEXT 275 0 "" }}}{EXCHG {PARA 264 "> \+ " 0 "" {MPLTEXT 1 0 27 "possiblemoves := proc(v,n):" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 42 " w:=[seq(0,i=1..8)];\n w[1] := v + [2,1];" }} {PARA 264 "> " 0 "" {MPLTEXT 1 0 20 " w[2] := v + [1,2];" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 21 " w[3] := v + [-2,1];" }}{PARA 264 "> \+ " 0 "" {MPLTEXT 1 0 21 " w[4] := v + [1,-2];" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 22 " w[5] := v + [-1,-2];" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 22 " w[6] := v + [-2,-1];" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 22 " w[7] := v + [-1,2]; " }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 21 " w[8] := v + [2,-1];" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 167 " for i from 1 to 8 do\n if ((0 < w[i][1]) and (w [i][1] < n+1) and (0 < w[i][2]) and (w[i][2] < n+1))\n then connect (\{v\},\{w[i]\}, G)\n end if;\n end do;\nend proc;" }}{PARA 272 " " 1 "" {TEXT -1 71 "Warning, `w` is implicitly declared local to proce dure `possiblemoves`\n" }}{PARA 272 "" 1 "" {TEXT -1 71 "Warning, `i` \+ is implicitly declared local to procedure `possiblemoves`\n" }}{PARA 270 "" 1 "" {XPPMATH 20 "6#>%.possiblemovesGf*6$%\"vG%\"nG6$%\"wG%\"iG 6\"F,C,>8$7#-%$seqG6$\"\"!/8%;\"\"\"\"\")>&F/6#F8,&9$F87$\"\"#F8F8>&F/ 6#F@,&F>F87$F8F@F8>&F/6#\"\"$,&F>F87$!\"#F8F8>&F/6#\"\"%,&F>F87$F8FLF8 >&F/6#\"\"&,&F>F87$!\"\"FLF8>&F/6#\"\"',&F>F87$FLFYF8>&F/6#\"\"(,&F>F8 7$FYF@F8>&F/6#F9,&F>F87$F@FYF8?(F6F8F8F9%%trueG@$3332F4&&F/6#F6F<2F\\p ,&9%F8F8F82F4&F]pFC2FcpF`p-%(connectG6%<#F><#F]p%\"GGF,F,F," }}} {EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 286 173 "Notice that the result will not display all the vertices that con nected to the initial vertex. Instead it displays the edge that is be ing connected to the initial vertex. " }}{PARA 264 "" 0 "" {TEXT 287 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 23 "possiblemoves([2,3],4);" } }{PARA 269 "" 1 "" {XPPMATH 20 "6#%#e4G" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 288 312 "The resulting vertice s of the initial vertex can be obtain by using the neighbors method. \+ This method will display all the vertices that are connecting to the i nitial vertex. Unfortunately, this does not tell me anything. I don' t want Maple to give me just a few vertices that connected to the init ial vertex." }}{PARA 264 "" 0 "" {TEXT 289 1 "\n" }{MPLTEXT 1 0 19 "ne ighbors([2,3],G);" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#<&7$\"\"$\"\"\"7 $F&F&7$\"\"%F)7$F)\"\"#" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }} {PARA 264 "" 0 "" {TEXT -1 94 "I'm hoping that edges(G) would tell me \+ something about all the edges that are being connected." }}{PARA 264 " " 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 9 "edges(G);" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#<&%#e3G%#e2G%#e1G%#e4G" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 181 "Finally, the following procedure chessTable will generate a chess table for the possiblemove s procedure that contains all the possible moves (in vertices) with th e given Size value." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> \+ " 0 "" {MPLTEXT 1 0 222 "chessTable:= proc(n): for i from 1 to n \n \+ do for j from 1 to n \n \+ do possiblemoves([i,j],n) \n od; \n \+ od;\n end proc;\n" }}{PARA 272 "" 1 "" {TEXT -1 68 "Warning, `i` is implicitly declared local to procedure `c hessTable`\n" }}{PARA 272 "" 1 "" {TEXT -1 68 "Warning, `j` is implici tly declared local to procedure `chessTable`\n" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#>%+chessTableGf*6#%\"nG6$%\"iG%\"jG6\"F+?(8$\"\"\"F.9$% %trueG?(8%F.F.F/F0-%.possiblemovesG6$7$F-F2F/F+F+F+" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 209 "By calling Size in chessTable, I am able to generate all the vertices on the che ss board. YES!!!!! This is what I want Maple to display. Hopefuly thi s will give me all the vertices that I needed to work with." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 26 "chess Table(Size);\nends(G);" }}{PARA 270 "" 1 "" {XPPMATH 20 "6#F7<$F>7$F*F'<$F>7$F*F)<$F<7$F)F.<$F77$F)F'<$F77$F)F&<$F-F7<$FB7$F*F *<$F?7$F)F)<$F " 0 "" {MPLTEXT 1 0 8 " draw(G);" }}{PARA 271 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6_q-% %TEXTG6$7$$\"+uio*G(!#5$\"+g5ZXoF)Q'[1,~2]6\"-%'POINTSG6#7$$\"+^zEe`F) $\"+a#zKW)F)-F$6$F1Q'[2,~4]F--F/6#7$$\"+Q*p,4$F)$\"+l^c5&*F)-F$6$7$$\" ++o1j()F)$\"+Tn`<[F)Q'[2,~5]F--F/6#F&-F$6$7$$\"+6;$eo*F)$\"+s))*o[#F)Q '[3,~1]F--F/6#FB-F/6#FL-F/6#7$$\"\"\"\"\"!$FenFen-F$6$FXQ'[1,~3]F--F$6 $7$$\"+7;$eo*F)$!+r))*o[#F)Q'[2,~2]F--F$6$7$$\"+-o1j()F)$!+Qn`<[F)Q'[2 ,~1]F--F/6#F\\o-F$6$7$$\"+zio*G(F)$!+a5ZXoF)Q'[4,~5]F--F/6#Fdo-F$6$7$$ \"+]zEe`F)$!+b#zKW)F)Q'[5,~1]F--F/6#F^p-F$6$7$$\"+Y*p,4$F)$!+i^c5&*F)Q '[5,~2]F--F/6#Fhp-F/6#Fbq-F$6$7$$\"+2?0zi!#6$!+%Gn-)**F)Q'[5,~3]F--F$6 $7$$!+[J\"Q(=F)$!+2D(G#)*F)Q'[5,~4]F--F/6#F^r-F$6$7$$!+:HzdUF)$!+D0F[! *F)Q'[5,~5]F--F/6#Fgr-F$6$7$$!+%*)RUP'F)$!+IC80xF)Q'[3,~2]F--F/6#F[t-F /6#Fas-F$6$7$$!+Y*p,4)F)$!+?D&y(eF)Q'[3,~3]F--F$6$7$$!+f[w(H*F)$!+FbC \"o$F)Q'[3,~4]F--F/6#Fgt-F$6$7$$!+8q9@**F)$!+QBL`7F)Q'[3,~5]F--F/6#F_u -F/6#7$$!+9q9@**F)$\"+IBL`7F)-F$6$FcvQ'[4,~1]F--F/6#Fiu-F/6#7$$!+e[w(H *F)$\"+GbC\"o$F)-F$6$F_wQ'[4,~2]F--F/6#7$$!+X*p,4)F)$\"+AD&y(eF)-F$6$F iwQ'[4,~3]F--F$6$7$$!+,*RUP'F)$\"+DC80xF)Q'[4,~4]F--F$6$7$$!+8HzdUF)$ \"+E0F[!*F)Q'[1,~4]F--F/6#Fcx-F/6#F[y-F/6#7$$!+YJ\"Q(=F)$\"+2D(G#)*F)- F$6$FgyQ'[1,~1]F--F$6$7$$\"+D>0ziFar$\"+%Gn-)**F)Q'[1,~5]F--F$6$F;Q'[2 ,~3]F--F/6#Faz-%'CURVESG6$7$FLF&-%'COLOURG6&%$RGBGFen$\"#5!\"\"Fen-F][ l6$7$F&F1F`[l-F][l6$7$F;F_wF`[l-F][l6$7$F;FcxF`[l-F][l6$7$FgyF[tF`[l-F ][l6$7$FLF;F`[l-F][l6$7$F;FgyF`[l-F][l6$7$FLFiwF`[l-F][l6$7$FLFbqF`[l- F][l6$7$FgtFgrF`[l-F][l6$7$F[yFiuF`[l-F][l6$7$FXFBF`[l-F][l6$7$FXFdoF` [l-F][l6$7$FXF[tF`[l-F][l6$7$FXF_uF`[l-F][l6$7$F&FgtF`[l-F][l6$7$F[tFh pF`[l-F][l6$7$F1F[tF`[l-F][l6$7$FgtF^pF`[l-F][l6$7$F;FiuF`[l-F][l6$7$F cvFgtF`[l-F][l6$7$FBFgtF`[l-F][l6$7$FgtFdoF`[l-F][l6$7$FgtFbqF`[l-F][l 6$7$F_wF_uF`[l-F][l6$7$FazF_uF`[l-F][l6$7$FcxF[tF`[l-F][l6$7$F[tF^rF`[ l-F][l6$7$FcvF\\oF`[l-F][l6$7$FcvF^rF`[l-F][l6$7$F_wFgrF`[l-F][l6$7$Fi wFiuF`[l-F][l6$7$F_uF^rF`[l-F][l6$7$F_uF\\oF`[l-F][l6$7$F[yF\\oF`[l-F] [l6$7$F_wFdoF`[l-F][l6$7$F;FazF`[l-F][l6$7$FiwFasF`[l-F][l6$7$F1FiwF`[ l-F][l6$7$FiwFhpF`[l-F][l6$7$F[yFgtF`[l-F][l6$7$FiuFgrF`[l-F][l6$7$Fiw F\\oF`[l-F][l6$7$FBFcxF`[l-F][l6$7$FcxFbqF`[l-F][l6$7$F^rF^pF`[l-F][l6 $7$F_uFasF`[l-F][l6$7$F1F^pF`[l-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3 " "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 1 0" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" " Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curv e 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29 " "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "C urve 36" "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "Curve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48 " "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "C urve 55" "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "Curve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67 " "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "C urve 74" "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "Curve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86 " "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "C urve 93" "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" }}}} {EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 92 "AHH! You would think that I would be giving up by now. Wait until you see the next section." }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 264 "" 0 "" {TEXT 276 0 "" }}}{PARA 264 "" 0 "" {TEXT 277 0 "" }}{SECT 0 {PARA 268 "" 0 "" {TEXT 278 13 "Knight's Tour" }} {PARA 264 "" 0 "" {TEXT 279 44 "With the help of Sonja Willis's proje ct on " }{TEXT 266 57 "Hamiltonian Paths and Cayley Digraphs of Algebr aic Group." }{TEXT 280 134 " I'm hoping that it would help me in find ing the tour for Maple to graph. The following codes are taken from S onja Willis's project." }}{PARA 264 "" 0 "" {TEXT 281 0 "" }}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 230 "continuepath := proc(Graph,path) \n local daugh;\n daugh:=sort([op(departures(path[1],Graph) minus \{ op(path)\})]);\n \n if daugh = []\n then RETURN ([path,fals e]);\n else RETURN ([[daugh[1],op(path)],true]);\n fi;\nend:" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 550 "backtrack := proc( Gra ph, origpath)\n local bad, daugh, position, path ;\n path := origpat h;\n do\n bad:=path [1];\n path:=path [2..nops(path)];\n if \+ path = []\n then RETURN ([path, false]);\n fi;\n #print (p ath);\n daugh:=sort([op(departures(path[1],Graph) minus \+ \{op(path)\})]);\n member (bad,daugh,'po sition');\n #print(`da-po-ba`,daugh,position,bad);\n if positio n < nops(daugh)\n then RETURN ([[daugh[position + 1],op(path)],tr ue]);\n fi;\n #print(`bac-path`,path);\n od;\nend:" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 502 "HamiltonianPath := proc(Graph,st art)\n local path, result;\n path := [start];\n do \n do\n \+ result := continuepath (Graph,path);\n path := result[1]; \n \+ # print (path);\n if result[2] = false \n then break;\n \+ fi;\n od ;\n \n if nops(result[1]) = nops(vertices(Graph) )\n then RETURN (path);\n fi ;\n \n result:=backtrack (Grap h,path);\n if result[2]=false \n then print (`NO PATH TRY ANOT HER VERTEX`); break ;\n else path :=result[1];\n fi;\n od;\ne nd:" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 186 "It is time for me to check out what this HamiltonianPath procedures would give me. By calling my original graph G and assigni ng an initial vertex, this is what HamiltonianPath gives me." }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 33 "tour \+ := HamiltonianPath(G,[1,1]);" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 270 "" 1 "" {XPPMATH 20 "6#>%%tourG7;7$\"\"\"\"\"&7$\"\"$\"\"% 7$F(F(7$F+F*7$F(F'7$F*\"\"#7$F(F*7$F+F'7$F0F07$F'F+7$F*F(7$F(F+7$F+F07 $F0F'7$F'F*7$F0F(7$F+F+7$F(F07$F*F*7$F+F(7$F0F+7$F'F07$F*F'7$F0F*7$F'F '" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 233 "It turns out that HamiltonianPath procedure does give me a path that connects all the vertices on my chess board. It works, b ut now, how am I going to transfer all these points (vertices) into a \+ grid table that I have always wanted?" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 239 "Since Maple cannot produc e a grid table, I'm hoping that matrix will give me some kind of outpu t that would be similar to the grid table. Then again, it seems as th ough matrix is the only thing that is close to a grid table. Worth a \+ try!" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 25 "m := matrix(Size,Size,0);" }}{PARA 269 "" 1 "" {XPPMATH 20 "6#>%\"mG-%'matrixG6#7'7'\"\"!F*F*F*F*F)F)F)F)" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 141 "I am crossing my finger and hoping that the following codes will produce t he right matrix that display the path that the Knight's tour gives." } }{PARA 264 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "> " 0 "" {MPLTEXT 1 0 136 "n := nops(tour):\n for i from 1 to n \n \+ do m[tour[n-i+1][1],tour[n-i+1][2]] := i; \n \+ od:" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 10 "matrix(m);" }} {PARA 269 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'\"\"\"\"\"%\"#6\"#;\" #D7'\"#7\"#<\"\"#\"\"&\"#57'\"\"$\"#?\"\"(\"#C\"#:7'\"#=\"#8\"#A\"\"* \"\"'7'\"#@\"\")\"#>\"#9\"#B" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 0 " " }}{PARA 264 "" 0 "" {TEXT -1 114 "YEA HEW!!!!!!!!!!!!!! This is exa ctly what I wanted since the beginning of the project. This is really exciting!" }}{PARA 264 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 385 "The following results are displayed by generating a 5 by 5 table. Notice that every time Maple generates, the results ar e different. The reason for this is that the HamiltonianPath is gener ating in a random form and it is depending on the points that Maple pi ck to generate the graph. The chronological number from 1 to Size-by-S ize represent the order in which the knight is moving." }}{PARA 264 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 264 "" 0 "" {XPPEDIT 18 0 "matrix ([[1, 10, 5, 18, 3], [14, 19, 2, 11, 6], [9, 22, 13, 4, 17], [20, 15, \+ 24, 7, 12], [23, 8, 21, 16, 25]]);" "6#-%'matrixG6#7'7'\"\"\"\"#5\"\"& \"#=\"\"$7'\"#9\"#>\"\"#\"#6\"\"'7'\"\"*\"#A\"#8\"\"%\"#<7'\"#?\"#:\"# C\"\"(\"#77'\"#B\"\")\"#@\"#;\"#D" }{TEXT -1 2 " " }{XPPEDIT 18 0 "ma trix([[1, 18, 5, 12, 3], [8, 13, 2, 17, 6], [19, 22, 7, 4, 11], [14, 9 , 24, 21, 16], [23, 20, 15, 10, 25]]);" "6#-%'matrixG6#7'7'\"\"\"\"#= \"\"&\"#7\"\"$7'\"\")\"#8\"\"#\"#<\"\"'7'\"#>\"#A\"\"(\"\"%\"#67'\"#9 \"\"*\"#C\"#@\"#;7'\"#B\"#?\"#:\"#5\"#D" }{TEXT -1 2 " " }{XPPEDIT 18 0 "matrix([[1, 4, 11, 16, 25], [12, 17, 2, 5, 10], [3, 20, 7, 24, 1 5], [18, 13, 22, 9, 6], [21, 8, 19, 14, 23]]);" "6#-%'matrixG6#7'7'\" \"\"\"\"%\"#6\"#;\"#D7'\"#7\"#<\"\"#\"\"&\"#57'\"\"$\"#?\"\"(\"#C\"#:7 '\"#=\"#8\"#A\"\"*\"\"'7'\"#@\"\")\"#>\"#9\"#B" }{TEXT -1 2 " " } {XPPEDIT 18 0 "matrix([[1, 14, 19, 8, 25], [6, 9, 2, 13, 18], [15, 20, 7, 24, 3], [10, 5, 22, 17, 12], [21, 16, 11, 4, 23]]);" "6#-%'matrixG 6#7'7'\"\"\"\"#9\"#>\"\")\"#D7'\"\"'\"\"*\"\"#\"#8\"#=7'\"#:\"#?\"\"( \"#C\"\"$7'\"#5\"\"&\"#A\"#<\"#77'\"#@\"#;\"#6\"\"%\"#B" }}}{EXCHG {PARA 264 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 264 "" 0 "" {TEXT 282 0 "" }}}{EXCHG {PARA 264 "" 0 "" {TEXT 265 14 "Final Thoughts" }} {PARA 264 "" 0 "" {TEXT 283 0 "" }}{PARA 264 "" 0 "" {TEXT 284 782 "WE LL, The project turns out to be as what I wanted it to be but the task did not reach its conclusion as easy as I thought. When I first sta rted the project, I did not know what to do and how to begin the task. Knight's tour seems to have a simple task, as I begin to explore the tour and with the helps of Stefan Erickson, I find out that the simpl e task become a really big task. The biggest challenge for me is to w rite a procedure that teaches Maple to move the initial vertex to its \+ final destination and then print out the results in a gridded board. \+ As you have read the step by step that I have written during the missi on in accomplishing the Knight's tour, it have taken me this long to \+ have mission accomplished! I am a happy man!! Thank you for followin g my task." }}{PARA 264 "" 0 "" {TEXT -1 147 "Special thanks to Profes sor J. Wavrik and Stefan Erickson for helping me with this mission. An d thanks Sonja Willis for her HamiltonianPath codes. " }}}}{MARK "5 7 \+ 1 0" 96 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }