[rbode]

Is the answer 4 and 13?

I have heard this riddle a long time ago and tried to program is but didn't finnish it. Today I found the riddle back on this forum and programmed it again. My program comes with 4 and 13 (as the only solution), is this correct ?

-Ronald

This is the program:

Sub main()

    For b = 2 To 98
        For a = 2 To 98
            If a + b < 100 Then
'               Debug.Print a; b,
                If Not P_knows(a * b) Then
'                   Debug.Print "P knows not",
                    If S_knows_that(a + b) Then
'                       Debug.Print "S knows that",
                        If P_knows_now(a * b) Then
'                           Debug.Print "P knows now",
                            If S_knows_now(a + b) Then
'                               Debug.Print "S knows now",
                                MsgBox Format(a) + ", " + Format(b)
        End If: End If: End If: End If: End If
'       Debug.Print
'       DoEvents
    Next a, b
    
End Sub

Function P_knows(Product As Integer)                    'Does P know the numbers?

    t = 0
    
    For I = 2 To Sqr(Product)                           'Sqr to exclude the same numbers (e.g. 8 = 2 * 4 and 4 * 2)
        If Product Mod I = 0 Then t = t + 1             'P doesn't know if you can divide it by more then one number
        If t > 1 Then Exit For                          'no need to check futher
    Next
    
    P_knows = t = 1
    
End Function

Function S_knows_that(Sum)                              'Does S know that P can't know the numbers?

    For I = 2 To Sum  2                                ' 2 to exclude the same numbers (e.g. 17 = 2 + 15 and 15 + 2)
        If P_knows(i * (Sum - i)) Then                  'for all the possible sums P should not be able to know the combination
            S_knows_that = False
            Exit Function
        End If
    Next i
    
    S_knows_that = True
        
End Function

Function P_knows_now(Product)                           'Does P know the two numbers after S knows that P can't know them?

    t = 0

    For I = 2 To Sqr(Product)
        If Product Mod I = 0 Then                       'P can only say that if there is just one combination
            If I + (Product  i) < 100 Then If S_knows_that(i + (Product  i)) Then t = t + 1
            If t > 1 Then Exit For                      'no need to check futher
        End If
    Next i
    
    P_knows_now = t = 1
            
End Function

Function S_knows_now(Sum)                               'Does S know the two numbers too after P knows them?

    t = 0

    For I = 2 To Sum  2                                'S can only say that if there is just one combination
        If P_knows_now(i * (Sum - i)) Then t = t + 1
        If t > 1 Then Exit For                          'no need to check futher
    Next i
    
    S_knows_now = t = 1
            
End Function