Gaussian Summing of Digits!

[Zness]

In honor of Carl Friedrich Gauss I wrote a sub that sums every DIGIT (not every integer) between zero and the integer you choose. Let's take the integer 13 for example:

1+2+3+4+5+6+7+8+9+'1+0'+'1+1'+'1+2'+'1+3' = 55

or...

1+2+3...+999,999+1,000,000 = 27,000,001

Give it a try! Also, let me know what you think.... If you enjoy summing up digits Gaussian style.

-------

Option Explicit
Sub Gauss()

    Dim x As Double
    Dim y As Integer
    Dim Answer As Double
    Dim StartTime As Double
    Dim EndTime As Double
    Dim GaussNumber As Long
    
    GaussNumber = Application.InputBox("Enter an integer. Press OK to sum every DIGIT between 0 and your Integer", _
        "Integer Entry", 0)
    If GaussNumber = 0 Then Exit Sub
    If GaussNumber = 1 Then
        MsgBox "Answer = " & GaussNumber & ".... duh."
        Exit Sub
    End If
        
    StartTime = Timer
    Application.ScreenUpdating = False
    Answer = 0
    For x = 0 To GaussNumber
        Select Case x
            Case 0 To 8
                For y = 1 To Len(CStr(x))
                    Answer = Answer + CInt(Mid(CStr(x), y, 1))
                Next y
            Case 9
                Answer = Answer + 9
                GoTo AdvanceX
            Case Else
                For y = 1 To Len(CStr(x))
                    Answer = Answer + CInt(Mid(CStr(x), y, 1))
                Next y
        End Select
AdvanceX:
    Next x
    Application.ScreenUpdating = True
    EndTime = Timer
    MsgBox "It took you " & Round(EndTime - StartTime, 2) & _
        " seconds to ""GET GAUSSIAN"" witchyo digits!", vbOKOnly, "Answer = " & Answer
        
End Sub

-----

Let me know what you think!

-Zness

 

[MarcelBeug]

There is a much faster way of calculating the Gaussian Sum Of Digits:

For the last digit of the integer, you sum 1 through digit (1+2+3 etc)
For the other digits of the integer, you sum 3 parts:
a. Digit x SUM(1:9) x 10^(digit number - 1) (where last digit = digit number 1; second last digit = digit number 2, etc).
b. Digit x (previous digits + 1).
c. SUM(1 through (digit-1)) x 10^(digit number - 1) (0 if digit <= 1).

The final outcome is the sum of outcomes for each digit.

----------------

Example integer: 903,047

Last digit (7): 1+2+3+4+5+6+7 = 28

Second last digit (4):
a. 4x(SUM(1:9)x10^1) = 4x45 = 180.
b. 4x(7+1) = 32.
c. SUM(1 through 4-1))x10^1 = (1+2+3)x10= 60.
Total: 180+32+60=272.

Third last digit (0):
a. 0x(SUM(1:9)x10^2) = 0x900 = 0.
b. 0x(47+1) = 0.
c. 0 (because digit<=1).

Fourth last digit (3):
a. 3x(SUM(1:9)x10^3) = 3x13,500 = 40,500.
b. 3x(047+1) = 144.
c. SUM(1 through 3-1)) x 10^3 = (1+2)x1,000 = 3,000.
Total: 40,500+144+3,000 = 43,644.

Fifth last digit (0) delivers 0 (just like third last digit)

Sixth last digit (9):
a. 9x(SUM(1:9)x10^5)= 9x2,250,000 = 20,250,000.
b. 9x(03047+1) = 9x3,048 = 27,432.
c. SUM(1 through 9-1)) X 10^5 = (1+2+3+4+5+6+7+8)x1,000 = 36x1,000 = 36,000.
Total: 20,250,000+27,432+36,000 = 23,877,432.

Gaussian Sum Of Digits for 903,047: 28 + 272 + 0 + 43,644 + 0 + 23,877,432 = 23,921,376.

 

[mikerickson]

Perhaps

Sub test()
    Dim GaussNumber As Long
    
    GaussNumber = Application.InputBox("Enter an integer. Press OK to sum every DIGIT between 0 and your Integer", "Integer Entry", Default:="13", Type:=1)
    If GaussNumber < 1 Then Exit Sub: Rem canceled
    
    MsgBox GaussSumTo(GaussNumber)
End Sub

Function GaussSumTo(N As Long)
    Dim i As Long
    For i = 1 To N
        GaussSumTo = GaussSumTo + GNumeralSum(i)
    Next i
End Function

Function GNumeralSum(aNumber As Variant) As Long
    If Len(CStr(aNumber)) < 2 Then
        GNumeralSum = Val(aNumber)
    Else
        GNumeralSum = Val(Left(CStr(aNumber), 1)) + GNumeralSum(Mid(CStr(aNumber), 2))
    End If
End Function

 

[MarcelBeug]

Perhaps

Nice recursion . How about "VBA-ing" my suggestion (2 posts up) for a fast solution?

 

[Blade Hunter]

Sub Gauss()
Dim X As Long, Y As Long, Z As Long
For X = 1 To InputBox("Enter an integer and press OK", "Gaussian input Entry", 0)
    For Y = 1 To Len(CStr(X))
        Z = Z + CLng(Mid(CStr(X), Y, 1))
    Next
Next
MsgBox "Answer = " & Z
End Sub

 

[Blade Hunter]

Was hoping to do it without the inner loop but I couldn't work out a way to use split() on 1 char rather than using an actual char to split on.

 

[MarcelBeug]

Let me know what you think!

Well, with all due respect I think it's not really Gaussian style to loop from 1 to the provided integer.


I adjusted your code to loop through just the number of digits in the provided integer. For explanation, see my post (5 posts up).

Option Explicit
Sub GaussMB()

    Dim x As Double
    Dim y As Integer
    Dim Digit As Integer
    Dim L As Integer
    Dim PreviousPlus1 As Long
    Dim PartA As Long
    Dim PartB As Long
    Dim PartC As Long
    Dim Answer As Double
    Dim StartTime As Double
    Dim EndTime As Double
    Dim GaussNumber As Long
    
    GaussNumber = Application.InputBox("Enter an integer. Press OK to sum every DIGIT between 0 and your Integer", _
        "Integer Entry", 0)
    If GaussNumber = 0 Then Exit Sub
    If GaussNumber = 1 Then
        MsgBox "Answer = " & GaussNumber & ".... duh."
        Exit Sub
    End If
        
    StartTime = Timer
    Application.ScreenUpdating = False
    L = Len(CStr(GaussNumber))
    Digit = CInt(Mid(CStr(GaussNumber), L, 1))
    PreviousPlus1 = Digit + 1
    Answer = 0
    For x = 1 To Digit
        Answer = Answer + x
    Next x
    For x = 1 To L - 1
        Digit = CInt(Mid(CStr(GaussNumber), L - x, 1))
        If Digit <> 0 Then
            PartA = Digit * 45 * x * 10 ^ (x - 1)
            PartB = Digit * PreviousPlus1
            PartC = 0
            If Digit > 1 Then
                For y = 1 To Digit - 1
                    PartC = PartC + y * 10 ^ x
                Next y
            End If
            Answer = Answer + PartA + PartB + PartC
            PreviousPlus1 = PreviousPlus1 + Digit * 10 ^ x
        End If
    Next x
    Application.ScreenUpdating = True
    EndTime = Timer
    MsgBox "It took you " & Round(EndTime - StartTime, 2) & _
        " seconds to ""GET GAUSSIAN"" witchyo digits!", vbOKOnly, "Answer = " & Answer
        
End Sub

 

[XOR LX]

Well, with all due respect I think it's not really Gaussian style to loop from 1 to the provided integer.

Agreed! And nice post, by the way.

Regards

 

[Zness]

Well, with all due respect I think it's not really Gaussian style to loop from 1 to the provided integer.
I adjusted your code to loop through just the number of digits in the provided integer. For explanation, see my post (5 posts up).

This thread is getting awesome! In response to your quote, the inspiration for me to attempt this code was this video....
https://www.youtube.com/watch?v=Dd81F6-Ar_0