VBA, lottery total combinations could be ended with sums (only sum list)

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motilulla

Well-known Member
Joined
Feb 13, 2008
Messages
2,422
Office Version
  1. 2010
Hello,

I am looking for how many total combinations could be made with sums. For example lottery EuroMillions has 50 numbers out of that 5 numbers is drawn so far formula =COMBIN(50,5) there are 2.118.760 total combinations can be made.

Now say for example if starting number "1" is fixed I mean if played numbers with only so it will generate =COMBIN(49,4) = 211.876 combinations now these combinations have sum from 15 to 240.

I am looking answer how will be the distribution of 211.876 combinations with each sum (15 to 240) I just want VBA that can list total combination with each of the sum

Please see the example below for example with sum 15 only will be possibly 1 combination with sum 15 = 1,2,3,4,5 and need to find till sum 240 ( only sum list )

SumPlaying Fix Num=1
SumCombinations
15​
1
16​
17​
18​
19​
20​
21​
22​
23​
24​
25​
26​
27​
28​
29​
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230​
231​
232​
233​
234​
235​
236​
237​
238​
239​
240​

Thank you all.

I am using Excel 2000

Regards,
Moti
 
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Marc L said:
And what should be the expected result if the list is fixing numbers 1 & 4 ?

Marc L, in this case fixing numbers "1 & 4" there would be left 48 numbers in the game, as the 2 & 3 will be excluded.

Out of the 48 fixing 2 there will be =COMBIN(46,3) =15.180 total combinations

Starting 1st set of 5 will be with min sum 1, 4, 5, 6, 7 = 23, and the last set of 5 will be with max sum 1, 4, 48, 49, 50 = 152 this is what I am thinking so...

Kind Regards
Moti
 
Upvote 0
Last but not least according to the previous post to paste to the top of the worksheet module :​
VBA Code: 
Const K = 5, U = 50
  Dim oDic As Object

Sub CountSumCombinate(L&, S&, P&, Optional N&)
    Dim A&
    For P = P To U - N
        A = S + P:  If L < K Then CountSumCombinate L + 1, A, P + 1 Else oDic(A) = oDic(A) + 1
    Next
End Sub

Sub Demo3()
    Dim C&, M$, S&, X
        [A1].CurrentRegion.Offset(1).Clear
    Do
        M = InputBox(vbLf & M & vbLf & vbLf & " Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
        X = Split(Application.Trim(M)):  M = "":  S = 0
    For C = 0 To UBound(X)
        If X(C) < 1 Or X(C) > U Then M = " Number between 1 and " & U & " only !": Beep: Exit For
        S = S + X(C)
    Next
        If M = "" Then If X(UBound(X)) > U - K + 1 + UBound(X) Then M = " Last number too high !": Beep
    Loop Until M = ""
        Set oDic = CreateObject("Scripting.Dictionary")
        CountSumCombinate UBound(X) + 2, S, X(UBound(X)) + 1, K - UBound(X) - 2
    If oDic.Count Then
        [A2].Resize(oDic.Count, 2).Value2 = Application.Transpose(Array(oDic.Keys, oDic.Items))
        oDic.RemoveAll
    End If
        Set oDic = Nothing
End Sub
 
Upvote 0
Missing check - not fixing more than 4 numbers - added in Demo3 :​
VBA Code: 
Sub Demo3()
    Dim C&, M$, S&, X
        [A1].CurrentRegion.Offset(1).Clear
    Do
            M = InputBox(vbLf & M & vbLf & vbLf & " Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
            X = Split(Application.Trim(M))
        If UBound(X) >= K - 1 Then
            M = " Maximum " & K - 1 & " numbers !":  Beep
        Else
            M = "":  S = 0
        For C = 0 To UBound(X)
            If X(C) < 1 Or X(C) > U Then M = " Number between 1 and " & U & " only !": Beep: Exit For
            S = S + X(C)
        Next
            If M = "" Then If X(UBound(X)) > U - K + 1 + UBound(X) Then M = " Last number too high !": Beep
        End If
    Loop Until M = ""
        Set oDic = CreateObject("Scripting.Dictionary")
        CountSumCombinate UBound(X) + 2, S, X(UBound(X)) + 1, K - UBound(X) - 2
    If oDic.Count Then
        [A2].Resize(oDic.Count, 2).Value2 = Application.Transpose(Array(oDic.Keys, oDic.Items))
        oDic.RemoveAll
    End If
        Set oDic = Nothing
End Sub
 
Upvote 0
Optimization for the Combinate procedure :​
VBA Code: 
Const K = 5, U = 50
  Dim oDic As Object

Sub CountSumCombinate(L&, S&, P&)
    Dim A&
    For P = P To U - K + L
        A = S + P:  If L < K Then CountSumCombinate L + 1, A, P + 1 Else oDic(A) = oDic(A) + 1
    Next
End Sub

Sub Demo3()
    Dim C&, M$, S&, X
        [A1].CurrentRegion.Offset(1).Clear
    Do
            M = InputBox(vbLf & M & vbLf & vbLf & " Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
            X = Split(Application.Trim(M))
        If UBound(X) >= K - 1 Then
            M = " Maximum " & K - 1 & " numbers !":  Beep
        Else
            M = "":  S = 0
        For C = 0 To UBound(X)
            If X(C) < 1 Or X(C) > U Then M = " Number between 1 and " & U & " only !": Beep: Exit For
            S = S + X(C)
        Next
            If M = "" Then If X(UBound(X)) > U - K + 1 + UBound(X) Then M = " Last number too high !": Beep
        End If
    Loop Until M = ""
        Set oDic = CreateObject("Scripting.Dictionary")
        CountSumCombinate UBound(X) + 2, S, X(UBound(X)) + 1
    If oDic.Count Then
        [A2].Resize(oDic.Count, 2).Value2 = Application.Transpose(Array(oDic.Keys, oDic.Items))
        oDic.RemoveAll
    End If
        Set oDic = Nothing
End Sub
 
Upvote 0
Marc L said:
Optimization for the Combinate procedure :​
Click to expand...
Superb! Marc L, I did not asked neither I thought it can be possible to get sum results fixing multiple numbers, you did amazing job I like it very much. ?
I appreciate your kind help :)


Marc L said:
As it's better with the screen updating desactivated so finally :​
VBA Code: 
Const K = 5
  Dim N&, R&, V(), W

Sub SumCombinate(L&, S&, T$, Optional P&)
    Dim A&, C$
    For P = P To UBound(W) + N * (P = 0)
        A = S + W(P):  C = T & W(P)
        If L < K Then SumCombinate L + 1, A, C & " ", P + 1 Else R = R + 1: V(R, 0) = A: V(R, 1) = C
    Next
End Sub

Sub Demo1()
        Dim M$, S&, X
    Do
            M = InputBox(vbLf & M & vbLf & vbLf & "Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
            X = Split(Application.Trim(M))
        If UBound(X) >= K - 1 Then
            M = "1 to " & K - 1 & " numbers only !":  Beep
        Else
                M = "":  S = 0:  W = [COLUMN(A:AX)]
            For R = 0 To UBound(X)
                If X(R) < 1 Or X(R) > 50 Then M = "Number(s) between 1 and 50 only !": Beep: Exit For
                S = S + X(R):  W(X(R)) = False
            Next
        End If
    Loop Until M = ""
        [A1].CurrentRegion.Offset(1).Clear
        ReDim V(1 To Application.Combin(50 - UBound(X) - 1, K - UBound(X) - 1), 1)
        N = K - UBound(X) - 2:  R = 0:  W = Filter(W, False, False)
        SumCombinate UBound(X) + 2, S, Join(X) & " "
    If R Then
            Application.ScreenUpdating = False
        With [A2].Resize(R, 2)
            .IndentLevel = 2
            .Columns(1).HorizontalAlignment = xlRight
            .Value2 = V
            .Sort .Cells(1), 1, Header:=2
        End With
            Application.ScreenUpdating = True
    End If
        Erase V, W
End Sub
Click to expand...
Marc L, May I ask you one more favour can you modify this post#14 macro (as per your last Post#26 VBA) so this also can generate combination only of the left numbers...

In this case fixing numbers "1 & 4" there would be left 48 numbers in the game, as the 2 & 3 will be excluded. Out of the 48 fixing 2 there will be =COMBIN(46,3) =15.180 total combinations

Starting 1st set of 5 will 1, 4, 5, 6, 7 and the last set of 5 will be 1, 4, 48, 49, 50

I love your idea generate all combinations with selected fix numbers of sums great idea

Please can you help?

Kind Regards
Moti
 
Upvote 0
Replace all the worksheet module with this code containing both ways :​
VBA Code: 
Const K = 5, U = 50
  Dim oDic As Object, R&, V()

Sub CountSumCombinate(L&, S&, P&)
    Dim A&
    For P = P To U - K + L
        A = S + P:  If L < K Then CountSumCombinate L + 1, A, P + 1 Else oDic(A) = oDic(A) + 1
    Next
End Sub

Sub SumCombinate(L&, S&, P&, T$)
    Dim A&, C$
    For P = P To U - K + L
        A = S + P:   C = T & P
        If L < K Then SumCombinate L + 1, A, P + 1, C & " " Else R = R + 1: V(R, 0) = A: V(R, 1) = C
    Next
End Sub

Sub Combinate(Optional Generate As Boolean)
        Dim M$, S&, X
        [A1].CurrentRegion.Offset(1).Clear
    Do
            M = InputBox(vbLf & M & vbLf & vbLf & " Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
            X = Split(Application.Trim(M))
        If UBound(X) >= K - 1 Then
            M = " Maximum " & K - 1 & " numbers !":  Beep
        Else
            M = "":  S = 0
        For R = 0 To UBound(X)
            If X(R) < 1 Or X(R) > U Then M = " Number between 1 and " & U & " only !": Beep: Exit For
            S = S + X(R)
        Next
            If M = "" Then If X(UBound(X)) > U - K + 1 + UBound(X) Then M = " Last number too high !": Beep
        End If
    Loop Until M = ""
    If Generate Then
            ReDim V(1 To Application.Combin(U - X(UBound(X)), K - UBound(X) - 1), 1)
            R = 0
            SumCombinate UBound(X) + 2, S, X(UBound(X)) + 1, Join(X) & " "
        If R Then
                 Application.ScreenUpdating = False
            With [A2].Resize(R, 2)
                .IndentLevel = 2
                .Columns(1).HorizontalAlignment = xlRight
                .Value2 = V
                .Sort .Cells(1), 1, Header:=2
            End With
                 Application.ScreenUpdating = True
        End If
            Erase V
    Else
            Set oDic = CreateObject("Scripting.Dictionary")
            CountSumCombinate UBound(X) + 2, S, X(UBound(X)) + 1
        If oDic.Count Then
            [A2].Resize(oDic.Count, 2).Value2 = Application.Transpose(Array(oDic.Keys, oDic.Items))
            oDic.RemoveAll
        End If
            Set oDic = Nothing
    End If
End Sub

Sub CountCombinationsBySum()
    Combinate
End Sub

Sub ListCombinationsBySum()
    Combinate True
End Sub
 
Last edited:
Upvote 0
Solution
Marc L said:
Replace all the worksheet module with this code containing both ways :​
VBA Code: 
Const K = 5, U = 50
  Dim oDic As Object, R&, V()

Sub CountSumCombinate(L&, S&, P&)
    Dim A&
    For P = P To U - K + L
        A = S + P:  If L < K Then CountSumCombinate L + 1, A, P + 1 Else oDic(A) = oDic(A) + 1
    Next
End Sub

Sub SumCombinate(L&, S&, P&, T$)
    Dim A&, C$
    For P = P To U - K + L
        A = S + P:   C = T & P
        If L < K Then SumCombinate L + 1, A, P + 1, C & " " Else R = R + 1: V(R, 0) = A: V(R, 1) = C
    Next
End Sub

Sub Combinate(Optional Generate As Boolean)
        Dim M$, S&, X
        [A1].CurrentRegion.Offset(1).Clear
    Do
            M = InputBox(vbLf & M & vbLf & vbLf & " Space delimited :", "Fix number(s)"):  If M = "" Then Exit Sub
            X = Split(Application.Trim(M))
        If UBound(X) >= K - 1 Then
            M = " Maximum " & K - 1 & " numbers !":  Beep
        Else
            M = "":  S = 0
        For R = 0 To UBound(X)
            If X(R) < 1 Or X(R) > U Then M = " Number between 1 and " & U & " only !": Beep: Exit For
            S = S + X(R)
        Next
            If M = "" Then If X(UBound(X)) > U - K + 1 + UBound(X) Then M = " Last number too high !": Beep
        End If
    Loop Until M = ""
    If Generate Then
            ReDim V(1 To Application.Combin(U - X(UBound(X)), K - UBound(X) - 1), 1)
            R = 0
            SumCombinate UBound(X) + 2, S, X(UBound(X)) + 1, Join(X) & " "
        If R Then
                 Application.ScreenUpdating = False
            With [A2].Resize(R, 2)
                .IndentLevel = 2
                .Columns(1).HorizontalAlignment = xlRight
                .Value2 = V
                .Sort .Cells(1), 1, Header:=2
            End With
                 Application.ScreenUpdating = True
        End If
            Erase V
    Else
            Set oDic = CreateObject("Scripting.Dictionary")
            CountSumCombinate UBound(X) + 2, S, X(UBound(X)) + 1
        If oDic.Count Then
            [A2].Resize(oDic.Count, 2).Value2 = Application.Transpose(Array(oDic.Keys, oDic.Items))
            oDic.RemoveAll
        End If
            Set oDic = Nothing
    End If
End Sub

Sub CountCombinationsBySum()
    Combinate
End Sub

Sub ListCombinationsBySum()
    Combinate True
End Sub
Click to expand...
Marc L, I am wonder to see the Count/List combinations by sum 2 in 1 VBA solution added with multiple fix numbers you have done far beyond what I ask in the opening Post#1 felling very happy.

I am so grateful to you for giving a best response and time you spent to solve it far better. ?

I wish you Good Luck.

Kind Regards
Moti :)
 
Upvote 0
​
Thanks. The logic used is exactly the same as in joeu2004 post #4, just revamped to a 'single loop' sub procedure like in your previous thread …​
​
The Dictionary way works only under Windows, can be avoided just using an array like joeu2004 did.​
 
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