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' Constructs Euler - and Magic Squares of order 9
' Based on Semi-Latin Squares of order 9

' Tested with Office 2007 under Windows 7

Sub CnstrSqrs9a()
   
    Dim b(2, 81), a(81), m(81), s8(32)

    Sheets("Klad1").Select
    
y = MsgBox("Locked", vbExclamation, "Routine CnstrSqrs9a")
End

    n2 = 0: n9 = 0: k1 = 1: k2 = 1
    s1 = 369
    
    t1 = Timer
    
    For j1 = 2 To 1009

Cells(2, 1).Value = j1

    For j2 = 1010 To 2017
    If j2 = j1 Then GoTo 20
        
        j10 = j1: j20 = 1: GoSub 100                        'Read Semi-Latin Square 1
        j10 = j2: j20 = 2: GoSub 100                        'Read Semi-Latin Square 2
        
        For j4 = 1 To 81
            a(j4) = b(1, j4) + 9 * b(2, j4) + 1             'Semi  Magic Square
''          m(j4) = CStr(b(1, j4)) + ", " + CStr(b(2, j4))  'Orthogonal  Square
        Next j4
        
        GoSub 300: If fl1 = 0 Then GoTo 20                  'Check identical numbers
                           
'       n9 = n9 + 1: GoSub 640              'Print results (selected numbers)
'       n9 = n9 + 1: GoSub 650              'Print results (squares)
'       n9 = n9 + 1: GoSub 600              'Print results (Euler Squares)
        n9 = n9 + 1: Cells(1, 1).Value = n9 'Counting
                     
''End

20  Next j2
    Next j1
    
    t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
    y = MsgBox(t10, vbInformation, "Routine CnstrSqrs9a")

End

'   Read Latin Squares (Line Format)

100 For i1 = 1 To 81
        b(j20, i1) = Sheets("AssLns9").Cells(j10, i1).Value
    Next i1
    
    Return
    
'   Check identical numbers
    
300 fl1 = 1
    For i1 = 1 To 81
       a2 = a(i1)
       For i2 = (1 + i1) To 81
           If a2 = a(i2) Then fl1 = 0: Return
       Next i2
    Next i1
    Return
   
'   Print results (Orthogonal Squares)

600 n1 = n1 + 1
    If n1 = 5 Then
        n1 = 1: k1 = k1 + 10: k2 = 1
    Else
        If n9 > 1 Then k2 = k2 + 10
    End If
    
    Cells(k1, k2 + 1).Select
    Cells(k1, k2 + 1).Font.Color = -4165632
    Cells(k1, k2 + 1).Value = n9
    
    i3 = 0
    For i1 = 1 To 9
        For i2 = 1 To 9
            i3 = i3 + 1
             Cells(k1 + i1, k2 + i2).Value = m(i3)
        Next i2
    Next i1
    Return
    
'   Print results (selected numbers)

640 Cells(n9, 82).Select
    For i1 = 1 To 81
        Cells(n9, i1).Value = a(i1)
    Next i1
    Cells(n9, 82).Value = n9
    Cells(n9, 83).Value = j1 - 1
    Cells(n9, 84).Value = j2 - 1
    Return

'   Print results (squares)

650 n1 = n1 + 1
    If n1 = 5 Then
        n1 = 1: k1 = k1 + 10: k2 = 1
    Else
        If n9 > 1 Then k2 = k2 + 10
    End If
    
    Cells(k1, k2 + 1).Select
    Cells(k1, k2 + 1).Font.Color = -4165632
    Cells(k1, k2 + 1).Value = n9
    
    i3 = 0
    For i1 = 1 To 9
        For i2 = 1 To 9
            i3 = i3 + 1
            Cells(k1 + i1, k2 + i2).Value = a(i3)
        Next i2
    Next i1
    Return
    
End Sub

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