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#1
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"possible number combinations" of different numbers of integers -.
what would the formula be to "see" all "possible number combinations" of any
given about of intigers (0-9) |
#2
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Depends what you define as "combination" but anyway - your
solution should be found he http://www-cs-faculty.stanford.edu/~knuth/news.html HTH sulprobil |
#3
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Assuming you mean that you have 9 digits, and you want to know how many
different numbers can be constructed by rearranging these digits, you want the number of permutations of 9 things taken 9 at a time. There are 362,880 such permutations. Are you sure you want to see all of them? There's no formula for this. It can be done with VBA. I posted the following message, with the code, on July 25, 2000. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The routine is generic, i.e. it isn't written specifically for a given population and set size.... It will do permutations or combinations. It uses a recursive routine to generate the subsets, one routine for combinations, a different one for permutations. To use it, you put the letter C or P (for combinations or permutations) in a cell. The cell below that contains the number of items in a subset. The cells below are a list of the items that make up the population. They could be numbers, letters and symbols, or words, etc. You select the top cell, or the entire range and run the sub. The subsets are written to a new sheet in the workbook. Option Explicit Dim vAllItems As Variant Dim Buffer() As String Dim BufferPtr As Long Dim Results As Worksheet Sub ListPermutations() Dim Rng As Range Dim PopSize As Integer Dim SetSize As Integer Dim Which As String Dim N As Double Const BufferSize As Long = 4096 Set Rng = Selection.Columns(1).Cells If Rng.Cells.Count = 1 Then Set Rng = Range(Rng, Rng.End(xlDown)) End If PopSize = Rng.Cells.Count - 2 If PopSize 2 Then GoTo DataError SetSize = Rng.Cells(2).Value If SetSize PopSize Then GoTo DataError Which = UCase$(Rng.Cells(1).Value) Select Case Which Case "C" N = Application.WorksheetFunction.Combin(PopSize, SetSize) Case "P" N = Application.WorksheetFunction.Permut(PopSize, SetSize) Case Else GoTo DataError End Select If N Cells.Count Then GoTo DataError Application.ScreenUpdating = False Set Results = Worksheets.Add vAllItems = Rng.Offset(2, 0).Resize(PopSize).Value ReDim Buffer(1 To BufferSize) As String BufferPtr = 0 If Which = "C" Then AddCombination PopSize, SetSize Else AddPermutation PopSize, SetSize End If vAllItems = 0 Application.ScreenUpdating = True Exit Sub DataError: If N = 0 Then Which = "Enter your data in a vertical range of at least 4 cells. " _ & String$(2, 10) _ & "Top cell must contain the letter C or P, 2nd cell is the number " _ & "of items in a subset, the cells below are the values from which " _ & "the subset is to be chosen." Else Which = "This requires " & Format$(N, "#,##0") & _ " cells, more than are available on the worksheet!" End If MsgBox Which, vbOKOnly, "DATA ERROR" Exit Sub End Sub Private Sub AddPermutation(Optional PopSize As Integer = 0, _ Optional SetSize As Integer = 0, _ Optional NextMember As Integer = 0) Static iPopSize As Integer Static iSetSize As Integer Static SetMembers() As Integer Static Used() As Integer Dim i As Integer If PopSize 0 Then iPopSize = PopSize iSetSize = SetSize ReDim SetMembers(1 To iSetSize) As Integer ReDim Used(1 To iPopSize) As Integer NextMember = 1 End If For i = 1 To iPopSize If Used(i) = 0 Then SetMembers(NextMember) = i If NextMember iSetSize Then Used(i) = True AddPermutation , , NextMember + 1 Used(i) = False Else SavePermutation SetMembers() End If End If Next i If NextMember = 1 Then SavePermutation SetMembers(), True Erase SetMembers Erase Used End If End Sub 'AddPermutation Private Sub AddCombination(Optional PopSize As Integer = 0, _ Optional SetSize As Integer = 0, _ Optional NextMember As Integer = 0, _ Optional NextItem As Integer = 0) Static iPopSize As Integer Static iSetSize As Integer Static SetMembers() As Integer Dim i As Integer If PopSize 0 Then iPopSize = PopSize iSetSize = SetSize ReDim SetMembers(1 To iSetSize) As Integer NextMember = 1 NextItem = 1 End If For i = NextItem To iPopSize SetMembers(NextMember) = i If NextMember iSetSize Then AddCombination , , NextMember + 1, i + 1 Else SavePermutation SetMembers() End If Next i If NextMember = 1 Then SavePermutation SetMembers(), True Erase SetMembers End If End Sub 'AddCombination Private Sub SavePermutation(ItemsChosen() As Integer, _ Optional FlushBuffer As Boolean = False) Dim i As Integer, sValue As String Static RowNum As Long, ColNum As Long If RowNum = 0 Then RowNum = 1 If ColNum = 0 Then ColNum = 1 If FlushBuffer = True Or BufferPtr = UBound(Buffer()) Then If BufferPtr 0 Then If (RowNum + BufferPtr - 1) Rows.Count Then RowNum = 1 ColNum = ColNum + 1 If ColNum 256 Then Exit Sub End If Results.Cells(RowNum, ColNum).Resize(BufferPtr, 1).Value _ = Application.WorksheetFunction.Transpose(Buffer()) RowNum = RowNum + BufferPtr End If BufferPtr = 0 If FlushBuffer = True Then Erase Buffer RowNum = 0 ColNum = 0 Exit Sub Else ReDim Buffer(1 To UBound(Buffer)) End If End If 'construct the next set For i = 1 To UBound(ItemsChosen) sValue = sValue & ", " & vAllItems(ItemsChosen(i), 1) Next i 'and save it in the buffer BufferPtr = BufferPtr + 1 Buffer(BufferPtr) = Mid$(sValue, 3) End Sub 'SavePermutation -------------------------------------------------------------------------------- On Tue, 31 Aug 2004 09:55:05 -0700, "rsdauer" wrote: what would the formula be to "see" all "possible number combinations" of any given about of intigers (0-9) |
#4
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Hi, sulprobil:
I wonder if most folks have the right tools to work with Knuth's files. I followed your link to his site. The links on the page are to GZ files (some kind of archive/zip file that I don't recognize), but luckily I have a program that can open GZ files. Once I got that far, I found the archive content to be a Post Script file. Since I have Adobe Acrobat, full version, I was able to convert that to a PDF file. On Tue, 31 Aug 2004 10:08:39 -0700, "sulprobil" wrote: Depends what you define as "combination" but anyway - your solution should be found he http://www-cs-faculty.stanford.edu/~knuth/news.html HTH sulprobil |
#5
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On further exploration, I found Knuth's page has a link to an unzipper,
GZIP.EXE, and another to GhostScript, which can be used to view the PS file. On Tue, 31 Aug 2004 10:08:39 -0700, "sulprobil" wrote: Depends what you define as "combination" but anyway - your solution should be found he http://www-cs-faculty.stanford.edu/~knuth/news.html HTH sulprobil |
#6
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Myrna Larson wrote...
I wonder if most folks have the right tools to work with Knuth's files. I followed your link to his site. The links on the page are to GZ files (some kind of archive/zip file that I don't recognize), . . . gzipped - standard archive format on all Unix/Linux/BSD systems, and incorporated into nearly all Windows archiving programs written from 2000 on. but luckily I have a program that can open GZ files. Once I got that far, I found the archive content to be a Post Script file. Since I have Adobe Acrobat, full version, I was able to convert that to a PDF file. You've already mentioned GhostScript as an alternative way to view PS files (or convert them to PDF, HTML or plain text). There's also a shareware PS viewer named RoPS and an open source viewer/converter named MakePDF (still in beta). --- Message posted from http://www.ExcelForum.com/ |
#7
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Hi, Harlan:
Since I've never used a Unix/Linus/BSD system (or a Mac), their file formats are all Greek to me. FWIW, WinZip v8 *can* handle the GZ format (as well as PowerDesk, the program I normally use). Thanks for the additional info on viewing PS files. I checked out RoPS. It works OK, but the down side (for me, considering the use I would get from it) is the cost: $45. I guess I'll stick to converting to PDF, since I have the full version of Acrobat 6. Myrna Larson On Tue, 31 Aug 2004 18:58:35 -0500, hgrove wrote: Myrna Larson wrote... I wonder if most folks have the right tools to work with Knuth's files. I followed your link to his site. The links on the page are to GZ files (some kind of archive/zip file that I don't recognize), . . . gzipped - standard archive format on all Unix/Linux/BSD systems, and incorporated into nearly all Windows archiving programs written from 2000 on. but luckily I have a program that can open GZ files. Once I got that far, I found the archive content to be a Post Script file. Since I have Adobe Acrobat, full version, I was able to convert that to a PDF file. You've already mentioned GhostScript as an alternative way to view PS files (or convert them to PDF, HTML or plain text). There's also a shareware PS viewer named RoPS and an open source viewer/converter named MakePDF (still in beta). --- Message posted from http://www.ExcelForum.com/ |
#8
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"Myrna Larson" wrote...
Since I've never used a Unix/Linus/BSD system (or a Mac), their file formats are all Greek to me. But you have a thorough understanding of .zip file layout? File formats are common across OS's using the same character set (i.e., files do differ EBCDIC vs ASCII, but don't differ much among ASCII-based OS's). FWIW, WinZip v8 *can* handle the GZ format (as well as PowerDesk, the program I normally use). As can PowerArchiver, which I normally use. These days I'd guess everything other than perhaps PkZip can support all compressed archive formats that have ever been. FWLIW, there's also bzip (.bz) format, which can usually attain greater compression that .zip or .gz. PowerArchiver supports it. |
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