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Piele\nUniversity of Wisconsin, Parkside\n900 Wood Road\ \nKenosha, WI 53141\npiele@cs.uwp.edu"], "Subtitle", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[TextData[ "Published in\nMathematica in Education and Research\nVol.4 No.1\nCopyright \ 1995 TELOS/Springer-Verlag"], "Subsubtitle", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "A very active discussion was held recently on the MathGroup List \n\ concerning solutions to the Lottery problem: Simulate the random draw of \n6 \ different numbers from a bin filled with 42 numbers. Several original \n\ solutions were submitted. As luck would have it, the elementary problem \n\ posed in this column last time was a slightly more difficult version of \nthe \ same problem. The challenge was to create a function ", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["SlickDeal[N,M]", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" \nwhich deals out ", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["N", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" hands of ", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["M", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ " cards each from a standard deck of 52 cards. \nSolutions that simulate \ the way cards are actually dealt after repeated \nshuffles and cuts were of \ particular interest.\n\nSince the Lottery problem generated so much interest, \ and it sets the \nstage for the ", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["SlickDeal", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" problem, lets begin with this problem.", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{10, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Lottery "], "Subsection", CellMargins->{{Inherited, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Lotto Problem", CellMargins->{{19, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[ " (Source - Robert B. Love, MathGroup, Mon, 26 Dec 94, in \n[mg358] )\n\n\ OK, time for a little fun. I can generate a list of random integers as \n", CellMargins->{{19, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["Table[Random[Integer,{1,42}],{6}] ", CellMargins->{{19, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ "and I get a list 6 elements long \ncontaining the integers from 1 to 42. \ But how do I make sure no elements \nare repeated?\n", CellMargins->{{19, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{19, 109}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Solutions with Packages"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "A few people suggested using functions found in the package DiscreteMath."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[" <{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "(* by Benno Puetz *)\nLottery1[m_,n_]:=RandomKSubset[Range[1,n],m]\n\ Lottery1[6,42]"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {3, 18, 21, 26, 28, 39}\ \>", "\<\ {3, 18, 21, 26, 28, 39}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "(* <{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "(* by Richard Mercer and Robert Dickau *)\nLottery2[m_,n_]:= \ Take[RandomPermutation[n],m]\nLottery2[6,42]\n"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {1, 27, 39, 42, 12, 18}\ \>", "\<\ {1, 27, 39, 42, 12, 18}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[TextData[{ StyleBox[ "It was also pointed out by Robert Dickau that by extracting the code \n\ written for ", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["RandomPermutation", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ ", one can write the following solution \nwithout the use of the package.", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "(* by extracting the code in DiscreteMath`Permutations` *)\n\ Lottery3[m_,n_]:= Take[Map[#[[2]]&,Sort[Array[{Random[],#}&,n]]],m]\n\ Lottery3[6,42]"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {6, 17, 23, 33, 30, 8}\ \>", "\<\ {6, 17, 23, 33, 30, 8}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "This is a nice functional solution. It works by: constructing an array of \n\ random real numbers; indexing them from 1 to n; sorting the random real \n\ numbers which produces a random permutation of the index numbers 1 to n; \n\ and picking off the first m integers in the permutation."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Solution by Trial and Error "], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "There were several submission that used the idea of trial and error. "], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "(* by Martin McClain *)\nLottery4[m_,n_]:=(len=0;While[len != m,\n \ hand = Table[Random[Integer,{1,n}],{m}];\n len = \ Length[Union[hand]]];\n hand);\n Lottery4[6,42] \n\ "], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {3, 32, 31, 28, 6, 29}\ \>", "\<\ {3, 32, 31, 28, 6, 29}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "A close examination of this solution shows that it would come to a hault \n\ if one tried to select 40 numbers from 42 instead of 6. It is very \nunlikely \ that 40 random integers from 1 to 42 will be unique. \n"], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Procedural solutions"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "A typical Pascal or C language solution to the Lottery problem would be \nto \ pick a random number from the list of numbers, delete it from the list \nand \ repeat the process on the smaller list until all m random numbers are \n\ selected. Here are some examples using this strategy."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "(* by Lou Talman *)\nLottery5[m_,n_]:=\n (num = Range[n]; \n Table[j = \ Random[Integer, {1, n}];\n k = num[[j]];\n num = \ Delete[num, j];\n k, {m}]);"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "Lottery5[6,42] \n \ "], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {34, 17, 1, 21, 30, 10}\ \>", "\<\ {34, 17, 1, 21, 30, 10}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "(* by Donald Darling *)\n\ Lottery6[m_,n_]:=(S={};CS=Range[n];For[j=1,j<=m,j++,\n \ AppendTo[S,x={CS[[ Random[Integer,{1,n-j+1}] ]]}];\n \ CS=Complement[CS,x] ];Flatten[S])\nLottery6[6,42] "], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {32, 23, 22, 17, 1, 10}\ \>", "\<\ {32, 23, 22, 17, 1, 10}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "(* by Steve Skiema. Taken from his algorithm in the package:\n \ DiscreteMath`Combinatorica` for RandomKSubsets and applied to this\n\ problem.*)\nLottery7[m_,n_]:=(s=Range[n];\n \ Table[x=Random[Integer,{1,i}];\n \ {s[[i]],s[[x]]}={s[[x]],s[[i]]};\n s[[i]],{i,n,n-m+1,-1}])\n\n\ Lottery7[6,42]"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {34, 15, 3, 42, 13, 17}\ \>", "\<\ {34, 15, 3, 42, 13, 17}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Rewrite Rule Solution"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Here is a rewrite rule solution which uses trial and error to build up \n\ the desired list. It of course would slow down for large m. "], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "(* by Tyler Perkins *)\nrules[num_, range_] = {\n (* Rule #1:\n \ Delete any repetition. \n Only need to look at last element! *)\n \ { s1___, e_, s2___, e_ } :> { s1, e, s2 },\n \n (* Rule #2:\n \ Otherwise append a new random number \n until long enough.*)\n \n \ {elems___} :> {elems, Random[Integer, {1,range}]} \n /; \ Length[{elems}] < num\n};"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["Lottery8[m_,n_]:= {} //. rules[m,n]\nLottery8[6,42]"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {30, 29, 25, 5, 24, 21}\ \>", "\<\ {30, 29, 25, 5, 24, 21}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["The shuffle solution"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "We can use the idea submitted by Tom Fournelle for creating a good card \n\ shuffle program (see ", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["SlickDeal", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ " below), to solve the Lottery problem as \nfollows: Consider the numbers \ as cards from 1 to 42. ", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["Mix[numbers]", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" by \ndoing a perfect shuffle followed by a random cut (", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["RotateLeft)", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[". Nest this\nprocess 10 times and (", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["Take", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[") the top 6 numbers.", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "(* extracted from Tom Fournell's SlickDeal solution *)\n\ Mix[x_List]:=RotateLeft[Transpose\n \ [Partition[x,Length[x]/2]]//Flatten, \n \ Random[Integer,{1,Length[x]}]]\n\n\ Lottery9[m_,n_]:=Take[Nest[Mix[#]&,Range[n],10],m]\nLottery9[6,42]\n"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData["\<\ {37, 12, 27, 1, 34, 32}\ \>", "\<\ {37, 12, 27, 1, 34, 32}\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Graphic Solution"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Finally, we end the discussion of the Lottery problem by generating a \n\ graphics model of the random selection process."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["Needs[\"Graphics`Graphics3D`\"]\n"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "(* selection the bin locations, create graphics *)\nrandpos[n_]:= \ Table[Random[], {n}, {3}];\nbin[n_,s_]:=ScatterPlot3D[randpos[n],\n \ DisplayFunction->Identity] /. {x__Point -> \n\t\t {Hue[s], \ PointSize[0.05], x} ,\n\t\t Identity->$DisplayFunction}"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell["", "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "LotteryG[m_,n_]:=(Show[bin[m,.1],bin[n-m,.5]]; (*Show all balls*)\n\n\ (*Select Random numbers*)\n\ 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The \nsolution will be judged on how well it simulates the way cards \ are \nactually dealt after repeated shuffles and cuts. 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Each shuffle is a perfect shuffle and each \ncut \ is made at random between the 10th and 42ed card. The second time the \ndeck \ is shuffled the ", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["slickDeal", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ " begins with the shuffled state of the deck \nand not with the orginal \ ordered set of cards. ", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["Cutting and shuffling the cards."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "cut[cards_]:= \n RotateLeft[cards,Random[Integer,{10,42}]]\n \n\ shuffle[cards_]:=\n Flatten[Partition[cards,26]//Transpose,1]\n \n\ cards=Distribute[{{c,d,h,s},Range[2,10]~Join~{J,Q,K,A}},List];\ndeck=cards;"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Dealing n hands of k cards each after cutting and shuffling a random \n\ number of times. "], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "\nslickDeal[n_,k_]:=Module[{numcuts},\n \n\tnumcuts= \ Random[Integer,{6,12}];\n deck=Nest[shuffle[cut[#]]&,deck,numcuts];\n \ \n Take[Partition[deck,k],n]]\n "], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["slickDeal[4,5]//TableForm"], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[OutputFormData[ "\<\ TableForm[{{{c, K}, {c, 7}, {s, 2}, {s, 5}, {d, 8}}, {{h, 10}, {d, J}, {c, 5}, {h, Q}, {s, 9}}, {{c, 6}, {d, A}, {d, K}, {h, 2}, {s, 6}}, {{d, 3}, {s, 10}, {h, J}, {h, 5}, {c, 2}}}]\ \>", "\<\ c c s s d K 7 2 5 8 h d c h s 10 J 5 Q 9 c d d h s 6 A K 2 6 d s h h c 3 10 J 5 2\ \>"], "Output", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, AspectRatioFixed->True] }, Open ]], Cell[TextData[ "It would be interesting to speculate which of these two methods comes \n\ closest to our human experience. Ross Moore pointed out, \"In practice \n\ hand-shuffled deals are NOT RANDOM. After just 2 or 3 riffles and a cut, \nit \ becomes virtually impossible to predict what will be dealt to whom. \nHowever \ there are bound to be many correlations between (i) certain pairs \nof cards \ in the new deal; and (ii) how they were played on the previous \ndeal using \ the same deck. "], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Comments by Ross Moore"], "Subsubsection", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "\nIt is an on-going problem in the bridge fraternity as to whether the \n\ computer programs that are being used actually work properly -- that is, \n\ produce \"random hands\"."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Let us get an appreciation for the essence of the problem. 52! is a big \n\ number: 8.06582... x 10^67. Divide by (13!)^4 if you like --we are still \n\ pretty big at: 5.36447 x 10^28."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "The MINIMUM requirement of our random number generator is that it \ngenerate \ at least this many distinct random numbers. Note that I state \nthis as a \ requirement of the `random number generator', not of the \ndealing \ algorithm."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Since a random number generator(RNG) can be `seeded' to guarantee that it \n\ produces the same sequence of (pseudo-)random numbers, then the seeding \n\ function needs to be able to accept at least as many seeds that produce \n\ different (sequences of) numbers as there are elements\nin the sample space \ (i.e. distinct deals, hence 10^(28+) )."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "We would also like each deal to be equally likely as any other, so some \n\ sort of uniformity of distribution is also required."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "However a dealing program needs to be able to do even more than this. \n\ Given one deal then the next should be entirely independent; that is, \neach \ deal should have equal probability of occurrence after any other. \nThus we \ need to be able to produce ( 10^(28+) )^2 distinct random numbers."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "A typical tournament session normally needs at least 24 deals; it is \n\ common to produce 32. World championship matches can be much longer."], "Text",\ CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "So to satisfy the purists, we need to be able to generate ( 10^(28+) \n)^32 \ distinct random numbers. My understanding is that such things DO NOT \nEXIST \ on present day computers."], "Text", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["New Problem"], "Subsection", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{16, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "The Lottery problem received the kind of participation I have been hoping \n\ for in this column---but have been unable to achieve. The advanced \nproblem \ posed last time got no response. Therefore, I am dropping the \nadvanced \ problem and posing one more approachable and solvable problem of \ninterest \ to a wider audience. So send in those Pearls, I need more. \nI'll also pick \ up a few along the way by keeping an eye on the MathGroup."], "Text", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{16, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[" SuperPrime Rib"], "Subsubsection", Evaluatable->False, CellLabelMargins->{{16, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Butchering Farmer John's cows always yields the best prime rib. You can \n\ tell prime ribs by looking at the digits lovingly stamped across them, \none \ by one, by FJ and the USDA. 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"Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{19, Inherited}, {8, 15}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 40}, CellHorizontalScrolling->False, PageBreakBelow->False, LineSpacing->{1, 1}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[EmptySquare]", CellMargins->{{18, Inherited}, {8, 12}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 50}, CellHorizontalScrolling->False, PageBreakBelow->False, LineSpacing->{1, 1}, CounterIncrements->"Subsubsection", AspectRatioFixed->True, FontFamily->"Times", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{7, 10}, {7, 7}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, CounterIncrements->"Text", AspectRatioFixed->True, FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{7, 10}, {6, 6}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, CounterIncrements->"SmallText", AspectRatioFixed->True, FontFamily->"Times", FontSize->10], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. Some attributes for these styles are actually set in FormatType Styles \ (in the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], PageWidth->Infinity, CellMargins->{{42, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", AspectRatioFixed->True, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], PageWidth->Infinity, CellMargins->{{42, 10}, {7, 5}}, CellEditDuplicate->True, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output", AspectRatioFixed->True, FontFamily->"Courier", FontSize->12], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, FontColor->RGBColor[1, 0, 0]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->12], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], PageWidth->Infinity, CellMargins->{{7, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 1}, FormatType->InputForm, CounterIncrements->"Graphics", AspectRatioFixed->True, ImageSize->{282, 287}, ImageMargins->{{34, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->9, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{7, 0}, {4, 1}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, AspectRatioFixed->True, StyleMenuListing->None, FontSize->12, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{7, 0}, {0, 4}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, TextAlignment->Center, LineSpacing->{1, 1}, AspectRatioFixed->True, StyleMenuListing->None, FontSize->12, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }], MacintoshSystemPageSetup->"\<\ 00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001 0000I00000400`<300000BL?00400@00000000000000060001T1T00000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)