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' Constructs 9 x 9 Composed Magic Squares for Prime Numbers (Part 1)
' Semi Magic Sub Squares

' Tested with Office 2007 under Windows 7

Sub Priem9b1()

Dim a1(1260), b1(187141), b(187141), c(36), a(36), a9(81)

y = MsgBox("Locked", vbCritical, "Routine Priem9b1")
End
    
    n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
    ShtNm1 = "Priem2"
    
    Sheets("Klad1").Select
    t1 = Timer

'   Generate Squares

For j100 = 3 To 36
s3 = Sheets("Lines3").Cells(j100, 10).Value     'MC3
s6 = 2 * s3
m1 = Sheets("Lines3").Cells(j100, 16).Value
m2 = Sheets("Lines3").Cells(j100, 17).Value

    For i1 = 1 To m2
        a1(i1) = Sheets(ShtNm1).Cells(i1, 3).Value
    Next i1

    Erase b1
    For i1 = m1 To m2
        b1(a1(i1)) = a1(i1)
    Next i1

'   Read Magic Center Square and Remove from b1()

    For i1 = 1 To 9
        a(i1) = Sheets("Lines3").Cells(j100, i1).Value
        b1(a(i1)) = 0
    Next i1
    
'   Assign to a9()
    
    n10 = 5: GoSub 750: n10 = 0
    Erase a

'   Generate Corner Squares

Cells(k1, 1).Select: Cells(k1, 1).Value = j100

For j31 = m1 To m2 / 4                                            'a(31)    Main Diagonal
If b1(a1(j31)) = 0 Then GoTo 310
If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 310
a(31) = a1(j31)

For j26 = m1 To m2                                                'a(26)
If b1(a1(j26)) = 0 Then GoTo 260
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)

For j21 = m1 To m2                                                'a(21)
If b1(a1(j21)) = 0 Then GoTo 210
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)

For j32 = m1 To m2                                                'a(32)    Square 1
If b1(a1(j32)) = 0 Then GoTo 320
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)

a(33) = s6 / 2 - a(31) - a(32)
If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
If b1(a(33)) = 0 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330

a(27) = -a(21) + a(31) + a(32)
If a(27) < a1(m1) Or a(27) > a1(m2) Then GoTo 270
If b1(a(27)) = 0 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270

a(25) = s6 / 2 + a(21) - a(26) - a(31) - a(32)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250

a(20) = s6 / 2 - a(26) - a(32)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200

a(19) = -a(21) + a(26) + a(32)
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190

For j16 = m1 To m2                                                'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)

For j11 = m1 To m2                                                'a(11)
If b1(a1(j11)) = 0 Then GoTo 110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)

a(6) = s6 - a(11) - a(16) - a(21) - a(26) - a(31)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60

For j17 = m1 To m2                                                'a(17)     Square 2
If b1(a1(j17)) = 0 Then GoTo 170
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)

a(18) = s6 / 2 - a(16) - a(17)
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180
If b1(a(18)) = 0 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180

a(12) = -a(6) + a(16) + a(17)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120

a(10) = s6 / 2 + a(6) - a(11) - a(16) - a(17)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100

a(5) = s6 / 2 - a(11) - a(17)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50

a(4) = -a(6) + a(11) + a(17)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40
If b1(a(4)) = 0 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40

'                     Exclude solutions with identical numbers

                      GoSub 800: If fl1 = 0 Then GoTo 5

                      n10 = n10 + 1
                      Select Case n10

                      Case 1
                             GoSub 750                              'Assign Sub Squares 1, 2
                             GoSub 900                              'Remove used primes
                             Erase b, c: GoTo 310
                      Case 2
                             GoSub 750                              'Assign Sub Squares 3, 4
                             GoSub 850                              'Double Check Identical Integers
                             If fl1 = 1 Then
                                    n9 = n9 + 1: GoSub 660          'Print Composed Squares
                             End If
                             Erase b, c: GoTo 1000                  'Only four Sub Squares required, next j100
                      End Select

5

    b(c(4)) = 0: c(4) = 0
40  b(c(5)) = 0: c(5) = 0
50  b(c(10)) = 0: c(10) = 0
100 b(c(12)) = 0: c(12) = 0
120 b(c(18)) = 0: c(18) = 0
180 b(c(17)) = 0: c(17) = 0
170 Next j17

    b(c(6)) = 0: c(6) = 0
60  b(c(11)) = 0: c(11) = 0
110 Next j11
    
    b(c(16)) = 0: c(16) = 0
160 Next j16

    b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(25)) = 0: c(25) = 0
250 b(c(27)) = 0: c(27) = 0
270 b(c(33)) = 0: c(33) = 0
330 b(c(32)) = 0: c(32) = 0
320 Next j32

    b(c(21)) = 0: c(21) = 0
210 Next j21

    b(c(26)) = 0: c(26) = 0
260 Next j26

    b(c(31)) = 0: c(31) = 0
310 Next j31


1000  n10 = 0
      Next j100

   t2 = Timer
    
   t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
   y = MsgBox(t10, 0, "Routine Priem9b1")

End

'   Print results (selected numbers)

640 Cells(n9, 9).Select
    For i1 = 1 To 81
        Cells(n9, i1).Value = a9(i1)
    Next i1
    Cells(n9, 82).Value = 3 * s3
    Return

'   Print results (squares 9 x 9)

660 n1 = n1 + 1
    If n1 = 3 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 = CStr(3 * s3)
    
    i3 = 0
    For i1 = 1 To 9
        For i2 = 1 To 9
            i3 = i3 + 1
            Cells(k1 + i1, k2 + i2).Value = a9(i3)
        Next i2
    Next i1
    
    Return
   
'    Exclude solutions with identical numbers a9()

850  fl1 = 1
     For j1 = 1 To 81
        a20 = a9(j1): If a20 = 0 Then GoTo 860
        For j2 = (1 + j1) To 81
            If a20 = a9(j2) Then fl1 = 0: Return
        Next j2
860  Next j1
     Return
     
'    Assign Sub Squares

750  Select Case n10

        Case 1
        
        'Top / Right

            a9(7) = a(4):   a9(8) = a(5):   a9(9) = a(6):
            a9(16) = a(10): a9(17) = a(11): a9(18) = a(12):
            a9(25) = a(16): a9(26) = a(17): a9(27) = a(18):
            
        'Bottom / Left
            
            a9(55) = a(19): a9(56) = a(20): a9(57) = a(21):
            a9(64) = a(25): a9(65) = a(26): a9(66) = a(27):
            a9(73) = a(31): a9(74) = a(32): a9(75) = a(33):
        
        Case 2

        'Top / Left

            a9(1) = a(6):   a9(2) = a(5):   a9(3) = a(4):
            a9(10) = a(12): a9(11) = a(11): a9(12) = a(10):
            a9(19) = a(18): a9(20) = a(17): a9(21) = a(16):
        
        'Bottom / Right
        
            a9(61) = a(21): a9(62) = a(20): a9(63) = a(19):
            a9(70) = a(27): a9(71) = a(26): a9(72) = a(25):
            a9(79) = a(33): a9(80) = a(32): a9(81) = a(31):
            
        Case 5: 'Center
            
            a9(31) = a(1):  a9(32) = a(2):  a9(33) = a(3):
            a9(40) = a(4):  a9(41) = a(5):  a9(42) = a(6):
            a9(49) = a(7):  a9(50) = a(8):  a9(51) = a(9):
     
     End Select
     
     Return

'    Exclude solutions with identical numbers a()

800  fl1 = 1
     For j1 = 1 To 36
        a20 = a(j1): If a20 = 0 Then GoTo 810
        For j2 = (1 + j1) To 36
            If a20 = a(j2) Then fl1 = 0: Return
        Next j2
810  Next j1
     Return

'    Remove used primes a() from available primes b1()

900  For i1 = 1 To 36
         b1(a(i1)) = 0
     Next i1
     Return

End Sub

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