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' Generates Semi Magic Squares of Subtraction (9 x 9)
' Part II, Resulting Magic Diagonals

' Tested with Office 365 under Windows 10

Sub CnstrSqrs9b()

Dim a(81), a0(9, 9), a1(9), a2(9), s(20)
Dim n(9, 2)
Dim a3(9, 9), a4(9, 9), a5(20), d1(9), d2(9)
Dim b(81), Line9(9)

y = MsgBox("Blocked", vbExclamation, "CnstrSqrs9b")
End

Sheets("Klad1").Select

n1 = 0: n9 = 0: k1 = 1: k2 = 1

ShtNm1 = "SemiLns9"
ShtNm2 = "ScrSht9"

t1 = Timer

For j100 = 1 To 2

        For i1 = 1 To 81
            a(i1) = Sheets(ShtNm1).Cells(j100, i1).Value
        Next i1
        s1 = 369
        Res9 = 41

'      Check Possible Diagonals
    
       GoSub 200: If fl1 = 0 Then GoTo 5    'Write Sets 'ScrSht9'
       GoSub 400: If n29 = 0 Then GoTo 5    'Check Valid Sets
      
''     n9 = n9 + 1: GoSub 750               'Print Semi Magic Squares
                                            'Related number of Magic Squares Shown (n29)
5

1000 Next j100

t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
    y = MsgBox(t10, 0, "Routine CnstrSqrs9b")
End
    
'   Check Possibility Diagonals (Magic)

200 fl1 = 1

    i2 = 1: i3 = 0
    For i1 = 1 To 81:
         i3 = i3 + 1: If i3 = 10 Then i3 = 1: i2 = i2 + 1
         a3(i2, i3) = a(i1)
    Next i1

    i190 = 0
    For i11 = 1 To 9
    For i12 = 1 To 9
    If i12 = i11 Then GoTo 220
    For i13 = 1 To 9
    If i13 = i11 Or i13 = i12 Then GoTo 230
    For i14 = 1 To 9
    If i14 = i11 Or i14 = i12 Or i14 = i13 Then GoTo 240
    For i15 = 1 To 9
    If i15 = i11 Or i15 = i12 Or i15 = i13 Or i15 = i14 Then GoTo 250
    For i16 = 1 To 9
    If i16 = i11 Or i16 = i12 Or i16 = i13 Or i16 = i14 Or i16 = i15 Then GoTo 260
    For i17 = 1 To 9
    If i17 = i11 Or i17 = i12 Or i17 = i13 Or i17 = i14 Or i17 = i15 Or i17 = i16 Then GoTo 270

    For i18 = 1 To 9
    If i18 = i11 Or i18 = i12 Or i18 = i13 Or i18 = i14 Or i18 = i15 Or i18 = i16 Or i18 = i17 Then GoTo 280
    For i19 = 1 To 9
    If i19 = i11 Or i19 = i12 Or i19 = i13 Or i19 = i14 Or i19 = i15 Or i19 = i16 Or i19 = i17 Or i19 = i18 Then GoTo 290
    
    s11 = a3(1, i11) + a3(2, i12) + a3(3, i13) + a3(4, i14) + a3(5, i15) + a3(6, i16) + a3(7, i17) + a3(8, i18) + a3(9, i19)
    If s11 <> s1 Then GoTo 290

Erase b, Line9
b(a3(1, i11)) = a3(1, i11)
b(a3(2, i12)) = a3(2, i12)
b(a3(3, i13)) = a3(3, i13)
b(a3(4, i14)) = a3(4, i14)
b(a3(5, i15)) = a3(5, i15)
b(a3(6, i16)) = a3(6, i16)
b(a3(7, i17)) = a3(7, i17)
b(a3(8, i18)) = a3(8, i18)
b(a3(9, i19)) = a3(9, i19)
    
q2 = 0
For q1 = 1 To 81
    If b(q1) = q1 Then
        q2 = q2 + 1: Line9(q2) = q1
    End If
Next q1
    
s12 = Line9(9) - Line9(8) + Line9(7) - Line9(6) + Line9(5) - Line9(4) + Line9(3) - Line9(2) + Line9(1)
If s12 <> Res9 Then GoTo 290
    
    i190 = i190 + 1
    
    Sheets(ShtNm2).Cells(i190, 11).Value = a3(1, i11)
    Sheets(ShtNm2).Cells(i190, 12).Value = a3(2, i12)
    Sheets(ShtNm2).Cells(i190, 13).Value = a3(3, i13)
    Sheets(ShtNm2).Cells(i190, 14).Value = a3(4, i14)
    Sheets(ShtNm2).Cells(i190, 15).Value = a3(5, i15)
    Sheets(ShtNm2).Cells(i190, 16).Value = a3(6, i16)
    Sheets(ShtNm2).Cells(i190, 17).Value = a3(7, i17)
    Sheets(ShtNm2).Cells(i190, 18).Value = a3(8, i18)
    Sheets(ShtNm2).Cells(i190, 19).Value = a3(9, i19)

290 Next i19
280 Next i18
270 Next i17
260 Next i16
250 Next i15
240 Next i14
230 Next i13
220 Next i12
210 Next i11

    If i190 < 2 Then fl1 = 0: Return

    n19 = 0
    For j11 = 1 To i190
 
    n20 = 9: Erase a5
    For i1 = 1 To 9
        a1(i1) = Sheets(ShtNm2).Cells(j11, i1 + 10).Value
    Next i1
    For i1 = 1 To 9   'First Line
        a5(i1) = a1(i1)
    Next i1
    
    For j12 = j11 + 1 To i190
    j300 = j12: GoSub 300: If fl2 = 0 Then GoTo 120

'      Write Set Diagonals to 'ScrSht9'

       For i1 = 1 To 2
            
            n19 = n19 + 1
            For i2 = 1 To 9
                 Sheets(ShtNm2).Cells(n19, i2 + 20).Value = a5(i2 + (i1 - 1) * 9)
            Next i2
            Sheets(ShtNm2).Cells(n19, 10 + 20).Value = i1
       Next i1

       n20 = n20 - 9
120    Next j12
       n20 = n20 - 9
110    Next j11

       If n19 < 2 Then fl1 = 0

Return
    
'   Construct Magic Set Diagonals
        
300 fl2 = 1

    For i1 = 1 To 9
        a2(i1) = Sheets(ShtNm2).Cells(j300, i1 + 10).Value
    Next i1

    n22 = 0
    For i1 = 1 To 9
    a20 = a2(i1)
    For i2 = 1 To n20
        If a20 = a5(i2) Then n22 = n22 + 1: i21 = i1: i22 = i2
    Next i2
    Next i1
    If n22 <> 1 Then fl2 = 0: Return    'Only one common allowed
    
 '  One Element Common (Center) ok
    
    n20 = n20 + 9: i22 = i22 + 9
    i2 = 0
    For i1 = n20 - 9 + 1 To n20
        i2 = i2 + 1
        a5(i1) = a2(i2)
    Next i1

    Return
        
'   Read Diagonals for Final Check

400
    n29 = 0:
    For j20 = 1 To n19 - 1 Step 2
        
        For i1 = 1 To 9
            d1(i1) = Sheets(ShtNm2).Cells(j20, i1 + 20).Value
            d2(i1) = Sheets(ShtNm2).Cells(j20 + 1, i1 + 20).Value
        Next i1

        Erase a4
        For i1 = 1 To 9
        For i2 = 1 To 9
            If a3(i1, i2) = d1(i1) Then a4(i1, i2) = 1
            If a3(i1, i2) = d2(i1) Then a4(i1, i2) = 2
        Next i2
        Next i1

        GoSub 450      'Check if transformation is possible
        
        
        If fl1 = 1 Then
            n29 = n29 + 1
            
'           Print Semi Magic Squares
'           Required Transformation Highlighted
            n9 = n9 + 1: GoSub 650

        End If
        
    Next j20

    Return

'   Check if transformation is possible

450 fl1 = 1

    For i1 = 1 To 9                 'rows
        n21 = 0: i41 = 0: i42 = 0
        For i2 = 1 To 9             'clmns
            If a4(i1, i2) <> 0 Then
               n21 = n21 + 1
               If n21 = 1 Then i41 = i2 Else i42 = i2
            End If
        Next i2
        
        If i41 = 0 Or i42 = 0 Then GoTo 460
        
        For i3 = i1 + 1 To 9
            If a4(i3, i41) = 0 And a4(i3, i42) = 0 Then
                                     'continue
            Else
               If a4(i3, i41) = a4(i1, i42) And a4(i3, i42) = a4(i1, i41) Then
                  Exit For          'ok
               Else
                  fl1 = 0: Return   'no match
               End If
            End If
        Next i3
        
460 Next i1

    Return
    
'   Print Semi Magic Squares
'   Required Transformation Highlighted

650 n2 = n2 + 1
    If n2 = 5 Then
        n2 = 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 = Nc9 ''n9
    Cells(k1, k2 + 2).Value = n29
 
    Cells(k1, k2 + 7).Value = j100  'Generator  Magic Lines
    
    i3 = 0
    For i1 = 1 To 9
        For i2 = 1 To 9
            i3 = i3 + 1
            Cells(k1 + i1, k2 + i2).Value = a(i3)
            
            Select Case a4(i1, i2)
               
                Case 1
                         
                    Range(Cells(k1 + i1, k2 + i2), Cells(k1 + i1, k2 + i2)).Select
                    With Selection.Interior
                        .Pattern = xlSolid
                        .PatternColorIndex = xlAutomatic
                        .ThemeColor = xlThemeColorDark1
                        .TintAndShade = -0.149998474074526
                        .PatternTintAndShade = 0
                    End With
                         
                Case 2
            
                    Range(Cells(k1 + i1, k2 + i2), Cells(k1 + i1, k2 + i2)).Select
                    With Selection.Interior
                        .Pattern = xlSolid
                        .PatternColorIndex = xlAutomatic
                        .ThemeColor = xlThemeColorAccent5
                        .TintAndShade = 0.599993896298105
                        .PatternTintAndShade = 0
                    End With
                    
                Case 0
            
            End Select
            
        Next i2
    Next i1
   
    Return
   
End Sub

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