Re: Re: Solving Alphametics with Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg38684] Re: [mg38640] Re: [mg38638] Solving Alphametics with Mathematica
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sat, 4 Jan 2003 07:27:32 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I evaluated the notebook below in a fresh kernel and this time it worked perfectly. I had to pinch myself to confirm I was not dreaming, but I can swear it did not work yesterday. Andrzej (************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info at 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[ 3922, 109]*) (*NotebookOutlinePosition[ 4579, 132]*) (* CellTagsIndexPosition[ 4535, 128]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[{\(<< NumericalMath`NMinimize`;\), "\[IndentingNewLine]", StyleBox[\(eq = 10^3\ b\ + \ 10^2\ a\ + 10\ s + \ e + 10^3\ b\ + \ 10^2 a + 10 l + l - 10^4 g - 10^3 a - 10^2 m - 10 e - s;\), FontFamily->"Monaco", FontSize->10], "\[IndentingNewLine]", \(ss = And @@ Union[ DeleteCases[ Flatten[ Outer[Abs[#1 - #2] \[GreaterEqual] 1 &, Variables[eq], Variables[eq]]], False], SameTest \[Rule] \((TrueQ[ Simplify[ First[#1] \[Equal] First[#2]]] &)\)];\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[\(NMinimize[{Abs[eq], \ a\ == \ 4\ && \ 0\ <= \ b\ <= \ 9\ && \n\ \ \ \ \ \ 0\ <= \ e\ <= \ 9\ && \ 1\ <= \ g\ <= \ 9\ && \ 0\ <= \ l\ <= \ 9\ && \n\ \ \ \ \ \ 0\ <= \ m\ <= \ 9\ && \ 0\ <= \ s\ <= \ 9\ && \ ss\ && \n\ \ \ \ \ \ Element[ a\ | \ b\ | \ e\ | \n\ \ \ \ \ \ \ \ g\ | \ l\ | \ m\ | \ s\ , \ Integers]}, \ Variables[eq]]\), FontFamily->"Monaco", FontSize->10]], "Input"], Cell[BoxData[ \({0.`, {a \[Rule] 4, b \[Rule] 7, e \[Rule] 3, g \[Rule] 1, l \[Rule] 5, m \[Rule] 9, s \[Rule] 8}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[\(NMinimize[{Abs[eq], \ 0 <= a <= 9\ && \ 1\ <= \ b\ <= \ 9\ && \n\ \ \ \ \ \ 0\ <= \ e\ <= \ 9\ && \ 1\ <= \ g\ <= \ 9\ && \ 0\ <= \ l\ <= \ 9\ && \n\ \ \ \ \ \ 0\ <= \ m\ <= \ 9\ && \ 0\ <= \ s\ <= \ 9\ && \ ss\ && \n\ \ \ \ \ \ Element[ a\ | \ b\ | \ e\ | \n\ \ \ \ \ \ \ \ g\ | \ l\ | \ m\ | \ s\ , \ Integers]}, \ Variables[eq]]\), FontFamily->"Monaco", FontSize->10]], "Input"], Cell[BoxData[ \({0.`, {a \[Rule] 4, b \[Rule] 7, e \[Rule] 3, g \[Rule] 1, l \[Rule] 5, m \[Rule] 9, s \[Rule] 8}}\)], "Output"] }, Open ]] }, FrontEndVersion->"4.2 for Macintosh", ScreenRectangle->{{24, 1152}, {0, 746}}, Evaluator->"Local", WindowSize->{520, 724}, WindowMargins->{{26, Automatic}, {Automatic, 0}} ] (******************************************************************* 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. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1754, 51, 685, 16, 171, "Input"], Cell[CellGroupData[{ Cell[2464, 71, 558, 11, 91, "Input"], Cell[3025, 84, 141, 2, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3203, 91, 559, 11, 91, "Input"], Cell[3765, 104, 141, 2, 27, "Output"] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************) On Saturday, January 4, 2003, at 07:54 AM, Andrzej Kozlowski wrote: > > Actually, I made a mistake in my message by copying the wrong code > from my notebook. The code: > > NMinimize[{Abs[eq], a == 4 && 0 <= b <= 9 && > 0 <= e <= 9 && 1 <= g <= 9 && 0 <= l <= 9 && > 0 <= m <= 9 && 0 <= s <= 9 && ss && > Element[a | b | e | > g | l | m | s , Integers]}, Variables[eq]] > > > also works on my machine, what does not work is: > > NMinimize[{Abs[eq], 0<=a<=9 && 1 <= b <= 9 && > 0 <= e <= 9 && 1 <= g <= 9 && 0 <= l <= 9 && > 0 <= m <= 9 && 0 <= s <= 9 && ss && > Element[a | b | e | > g | l | m | s , Integers]}, Variables[eq]] > > However, the latter code seem to work on Allan's Microsoft Windows > version of 4.2, which isn't any newer than mine (?) > > On Saturday, January 4, 2003, at 04:11 AM, Daniel Lichtblau wrote: > >> >>> [...] and then tried: >>> >>> NMinimize[{Abs[eq], a == 4 && 0 <= b <= 9 && >>> 0 <= e <= 9 && 1 <= g <= 9 && 0 <= l <= 9 && >>> 0 <= m <= 9 && 0 <= s <= 9 && ss && >>> Element[a | b | e | >>> g | l | m | s , Integers]}, Variables[eq]] >>> >>> but disappointingly NMinimize was unable to find any solution that >>> gave >>> 0 for the minimum of Abs. >> >> You need to upgrade (to our in-house development kernel). >> >> In[6]:= NMinimize[{Abs[eq], a == 4 && 0 <= b <= 9 && >> 0 <= e <= 9 && 1 <= g <= 9 && 0 <= l <= 9 && >> 0 <= m <= 9 && 0 <= s <= 9 && ss && >> Element[a | b | e | >> g | l | m | s , Integers]}, Variables[eq]] >> >> Out[6]= {0., {a -> 4, b -> 7, e -> 3, g -> 1, l -> 5, m -> 9, s -> 8}} >> >> >> Daniel >> >> > Andrzej Kozlowski > Yokohama, Japan > http://www.mimuw.edu.pl/~akoz/ > http://platon.c.u-tokyo.ac.jp/andrzej/ > >