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Brute Force Statistics

I have one of those RSA devices that helps me log in to work. I noticed that there always seems to be duplicate digits on the display as in the picture above.

So I wondered what the odds of this occurring are? I'm good at statistics and could probably have figured it out, but one thing you can use Excel VBA for is to brute force some statistical calculations.

So here is the code I used.



Sub brute_force()

'This routine will brute force calculate the number of duplicates

'that will appear in a 6 digit random RSA SecureID

Dim i, snum, snum2, lDups, j, bNoDups



For i = 0 To 999999

    'The display goes from 000000 to 999999

    snum = Format(i, "000000") 'add leading zeroes

    

    bNoDups = False ' this was used for debugging

    For j = 0 To 9 ' for each digit

        

        snum2 = Replace(snum, j, "") ' delete the digit

        If Len(snum2) < 5 Then '

            ' if after deleting a number says 0 there would be 5 digits left if no dups

            ' and < 5 if there are dups

            lDups = lDups + 1 'count the dups

            bNoDups = True ' set flag (for testing

            Exit For ' get out this is a dup

        End If

        

    Next

    'If bNoDups = False Then Stop ' used for debugging

    

Next

MsgBox "Odds are " & Format(lDups / 1000000, "#0.0%") ' the odds are the number of dups divided

                                                      ' by number of trials



End Sub

The following is displayed:

84.9%

If you have any questions on this contact me via twitter @AlecBerg

As an exercise try to develop the code to display the probability for the Birthday Problem

If you have the statistics solution to this problem send it to me and I'll post it here. If you have any statistical question to brute force send it to