DefDbl A-Z

Dim crlf$, ct(6), cw(10)

Function mform$(x, t$)

  a$ = Format$(x, t$)

  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$

  mform$ = a$

End Function

Private Sub Form_Load()

 ChDir "C:Program Files (x86)DevStudioVBprojectslooble"

 Text1.Text = ""

 crlf$ = Chr(13) + Chr(10)

 Form1.Visible = True

 DoEvents

 

 mo = 1: da = 1: ye = 1900

 GoSub GregToJD

 j0 = jd

 mo = 12: da = 31: ye = 1999

 GoSub GregToJD

 j1 = jd

 For j = j0 To j1

   jd = j

   GoSub JDToGreg

   s$ = Right("0" + LTrim(Str(mo)), 2) + Right("0" + LTrim(Str(da)), 2) + Right(Str(ye), 2)

   diffnums = 0

   For i = 1 To Len(s$)

     If InStr(s$, Mid(s$, i, 1)) = i Then diffnums = diffnums + 1

   Next

   ct(diffnums) = ct(diffnums) + 1

 Next

 

 For i = 0 To 6

  Text1.Text = Text1.Text & i & Str(ct(i)) & crlf

 Next

 Text1.Text = Text1.Text & " done"

 

 Exit Sub

 

GregToJD:

10100 Rem :greg mo/da/ye --> jd at noon

10110 GoSub JulToJD

10120 jd = jd + 2 - Int(cw(1) / 100) + Int(cw(1) / 400)

10130 Return

JulToJD:

10150 Rem :jul mo/da/ye --> jd at noon

10160 cw(0) = mo: cw(1) = ye: If mo < 3 Then cw(0) = mo + 12: cw(1) = ye - 1

10170 jd = Int(365.25 * cw(1)) + Int(30.61 * (cw(0) + 1)) + da + 1720995!

10180 Return

JDToGreg:

10200 Rem:noon jd-->greg mo/da/ye

10210 cw(0) = Int((jd - 1867216.25) / 36524.25)

10220 cw(0) = jd + 1 + cw(0) - Int(cw(0) / 4)

10230 GoTo CommonFromJD

JTToJul:

10240 Rem : noon jd-->jul mo/da/ye

10250 cw(0) = jd

CommonFromJD:

10260 cw(0) = cw(0) + 1524

10265 cw(1) = Int((cw(0) - 122.1) / 365.25)

10270 cw(2) = Int(365.25 * cw(1))

10275 cw(3) = Int((cw(0) - cw(2)) / 30.6001)

10280 da = cw(0) - cw(2) - Int(30.61 * cw(3))

10285 ye = cw(1) - 4716

10290 mo = cw(3) - 1: If mo > 12 Then mo = mo - 12: ye = ye + 1

10295 Return

 

End Sub

finds these counts:

0 0
1 1
2 159
3 3203
4 13791
5 15470
6 3900

adding up to 36524, the number of days between Jan 1, 1900, and Dec 31, 1999 or between Jan 1, 2000, and Dec 31, 2099.

If however we wanted 2000 through 2099, we'd need to count in another Feb 29, 2000 (290200) making the 3 count equal 3204. 

Parts b and c:

Using the counts of occurrences as weights for the counts of digits, the weighted sum is 165842; then dividing by the total of 36524 of the weights, gives an average of  4.540630818092214 different digits for a date, the average k. This is for the years 1900-1999 or for 2100-2199, as 1900 and 2100 are non-leap years.

However, to be exact about it, the 21st century really is from 2001 through 2100, being forced into the precedent set by there being no year zero so the first century began with year 1. So the 21st century actually fits the previous average, while the 20th century (1901-2000) had a full complement of 25 leap years, to be described below.

The new stats:

0 0
1 1
2 159
3 3204
4 13791
5 15470
6 3900

make the average   165845/36525 ~= 4.540588637919234, for the 20th century (1901-2000), or for the popular conception of the 21st century (2000-2099).