Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.

Cheryl gave them a list of ten possible dates:

     May 15,     May 16,     May 19
     June 17,    June 18
     July 14,    July 16
     August 14,  August 15,  August 17

Cheryl then tells Albert the   month   of birth,   and Bernard the   day   (of the month)   of birth.

 1)  Albert:   I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
 2)  Bernard:  At first I don't know when Cheryl's birthday is, but I know now.
 3)  Albert:   Then I also know when Cheryl's birthday is.



Task
Write a computer program to deduce, by successive elimination, Cheryl's birthday.



Related task

 Sum and Product Puzzle


References
 Wikipedia article of the same name.
 Tuple Relational Calculus


Private Sub exclude_unique_days(w As Collection)
    Dim number_of_dates(31) As Integer
    Dim months_to_exclude As New Collection
    For Each v In w
        number_of_dates(v(1)) = number_of_dates(v(1)) + 1
    Next v
    For i = w.Count To 1 Step -1
        If number_of_dates(w(i)(1)) = 1 Then
            months_to_exclude.Add w(i)(0)
            w.Remove i
        End If
    Next i
    For Each m In months_to_exclude
        exclude_month w, m
    Next m
End Sub
Private Sub exclude_month(x As Collection, v As Variant)
    For i = x.Count To 1 Step -1
        If x(i)(0) = v Then x.Remove i
    Next i
End Sub
Private Sub exclude_non_unique_days(w As Collection)
    Dim number_of_dates(31) As Integer
    For Each v In w
        number_of_dates(v(1)) = number_of_dates(v(1)) + 1
    Next v
    For i = w.Count To 1 Step -1
        If number_of_dates(w(i)(1)) > 1 Then
            w.Remove i
        End If
    Next i
End Sub
Private Sub exclude_non_unique_months(w As Collection)
    Dim months As New Collection
    For Each v In w
        On Error GoTo 1
        months.Add v(0), v(0)
    Next v
1:
    For i = w.Count To 1 Step -1
        If w(i)(0) = v(0) Then
            w.Remove i
        End If
    Next i
End Sub
Public Sub cherylsbirthday()
    Dim v As New Collection
    s = "May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17"
    t = Split(s, ",")
    For Each u In t
        v.Add Split(Trim(u), " ")
    Next u
    '1) Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
    exclude_unique_days v
    '2) Bernard: At first I don't know when Cheryl's birthday is, but I know now.
    exclude_non_unique_days v
    '3) Albert: Then I also know when Cheryl's birthday is.
    exclude_non_unique_months v
    Debug.Print v(1)(0); " "; v(1)(1)
End Sub