' Generates Unique Borders for Concentric Magic Squares of order 9

' Tested with Office 2007 under Windows 7

```Sub MgcSqr9d2()

Dim a1(32), a(81), b1(81), b(81), c(81)

y = MsgBox("Locked", vbCritical, "Routine Priem9d2")
End

k1 = 1: k2 = 1: n1 = 0: n2 = 0: n9 = 0

'   Define variables

a1(1) = 1:   a1(2) = 2:   a1(3) = 3:   a1(4) = 4:   a1(5) = 5:   a1(6) = 6:   a1(7) = 7:
a1(8) = 8:   a1(9) = 9:   a1(10) = 10: a1(11) = 11: a1(12) = 12: a1(13) = 13: a1(14) = 14:
a1(15) = 15: a1(16) = 16: a1(17) = 66: a1(18) = 67: a1(19) = 68: a1(20) = 69: a1(21) = 70:
a1(22) = 71: a1(23) = 72: a1(24) = 73: a1(25) = 74: a1(26) = 75: a1(27) = 76: a1(28) = 77:
a1(29) = 78: a1(30) = 79: a1(31) = 80: a1(32) = 81:

For i1 = 1 To 32
b1(a1(i1)) = a1(i1)
Next i1

m1 = 1: m2 = 32: s1 = 369: p2 = 82

t1 = Timer

'   Generate Border

For j81 = m2 To m1 Step -1                                            'a(81)
If b(a1(j81)) = 0 Then b(a1(j81)) = a1(j81): c(81) = a1(j81) Else GoTo 810
a(81) = a1(j81)

a(1) = p2 - a(81): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10

For j73 = j81 - 1 To m1 Step -1                                       'a(73)
If b(a1(j73)) = 0 Then b(a1(j73)) = a1(j73): c(73) = a1(j73) Else GoTo 730
a(73) = a1(j73)

a(9) = p2 - a(73):
If a(9) > a(73) Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90

For j80 = m2 To m1 Step -1                                            'a(80)
If b(a1(j80)) = 0 Then b(a1(j80)) = a1(j80): c(80) = a1(j80) Else GoTo 800
a(80) = a1(j80)

a(8) = p2 - a(80): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80

For j79 = j80 - 1 To m1 Step -1                                       'a(79)
If b(a1(j79)) = 0 Then b(a1(j79)) = a1(j79): c(79) = a1(j79) Else GoTo 790
a(79) = a1(j79)

a(7) = p2 - a(79): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70

For j78 = j79 - 1 To m1 Step -1                                       'a(78)
If b(a1(j78)) = 0 Then b(a1(j78)) = a1(j78): c(78) = a1(j78) Else GoTo 780
a(78) = a1(j78)

a(6) = p2 - a(78): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60

For j77 = j78 - 1 To m1 Step -1                                       'a(77)
If b(a1(j77)) = 0 Then b(a1(j77)) = a1(j77): c(77) = a1(j77) Else GoTo 770
a(77) = a1(j77)

a(5) = p2 - a(77): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50

For j76 = j77 - 1 To m1 Step -1                                       'a(76)
If b(a1(j76)) = 0 Then b(a1(j76)) = a1(j76): c(76) = a1(j76) Else GoTo 760
a(76) = a1(j76)

a(4) = p2 - a(76): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40

For j75 = j76 - 1 To m1 Step -1                                       'a(75)
If b(a1(j75)) = 0 Then b(a1(j75)) = a1(j75): c(75) = a1(j75) Else GoTo 750
a(75) = a1(j75)

a(3) = p2 - a(75): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30

a(74) = s1 - a(73) - a(75) - a(76) - a(77) - a(78) - a(79) - a(80) - a(81)
If a(74) < a1(m1) Or a(74) > a1(m2) Then GoTo 740
If b1(a(74)) = 0 Then GoTo 740
If a(74) > a(75) Then GoTo 740
If b(a(74)) = 0 Then b(a(74)) = a(74): c(74) = a(74) Else GoTo 740

a(2) = p2 - a(74): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20

For j72 = m2 To m1 Step -1                                            'a(72)
If b(a1(j72)) = 0 Then b(a1(j72)) = a1(j72): c(72) = a1(j72) Else GoTo 720
a(72) = a1(j72)

a(64) = p2 - a(72): If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640

For j63 = j72 - 1 To m1 Step -1                                       'a(63)
If b(a1(j63)) = 0 Then b(a1(j63)) = a1(j63): c(63) = a1(j63) Else GoTo 630
a(63) = a1(j63)

a(55) = p2 - a(63): If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550

For j54 = j63 - 1 To m1 Step -1                                       'a(54)
If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
a(54) = a1(j54)

a(46) = p2 - a(54): If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460

For j45 = j54 - 1 To m1 Step -1                                       'a(45)
If b(a1(j45)) = 0 Then b(a1(j45)) = a1(j45): c(45) = a1(j45) Else GoTo 450
a(45) = a1(j45)

a(37) = p2 - a(45): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370

For j36 = j45 - 1 To m1 Step -1                                       'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a(36) = a1(j36)

a(28) = p2 - a(36): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280

For j27 = j36 - 1 To m1 Step -1                                       'a(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a(27) = a1(j27)

a(19) = p2 - a(27): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190

a(18) = s1 - a(9) - a(27) - a(36) - a(45) - a(54) - a(63) - a(72) - a(81)
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180
If b1(a(18)) = 0 Then GoTo 180
If a(18) > a(27) Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180

a(10) = p2 - a(18): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100

'                           Exclude solutions with identical numbers (Back Check)

GoSub 1800: If fl1 = 0 Then GoTo 5

n9 = n9 + 1: GoSub 1640 'Print results (selected numbers)
'                           n9 = n9 + 1: GoSub 1650 'Print results (squares)
'                           n9 = n9 + 1: Cells(1, 1).Value = n9    'counting

'                           Erase b, c: GoTo 810    'Print only first square for j81

5

b(c(10)) = 0: c(10) = 0
100     b(c(18)) = 0: c(18) = 0
180     b(c(19)) = 0: c(19) = 0
190     b(c(27)) = 0: c(27) = 0
270     Next j27

b(c(28)) = 0: c(28) = 0
280     b(c(36)) = 0: c(36) = 0
360     Next j36

b(c(37)) = 0: c(37) = 0
370     b(c(45)) = 0: c(45) = 0
450     Next j45

b(c(46)) = 0: c(46) = 0
460     b(c(54)) = 0: c(54) = 0
540     Next j54

b(c(55)) = 0: c(55) = 0
550     b(c(63)) = 0: c(63) = 0
630     Next j63

b(c(64)) = 0: c(64) = 0
640     b(c(72)) = 0: c(72) = 0
720     Next j72

b(c(2)) = 0: c(2) = 0
20      b(c(74)) = 0: c(74) = 0
740     b(c(3)) = 0: c(3) = 0
30      b(c(75)) = 0: c(75) = 0
750     Next j75

b(c(4)) = 0: c(4) = 0
40      b(c(76)) = 0: c(76) = 0
760     Next j76

b(c(5)) = 0: c(5) = 0
50      b(c(77)) = 0: c(77) = 0
770     Next j77

b(c(6)) = 0: c(6) = 0
60      b(c(78)) = 0: c(78) = 0
780     Next j78

b(c(7)) = 0: c(7) = 0
70      b(c(79)) = 0: c(79) = 0
790     Next j79

b(c(8)) = 0: c(8) = 0
80      b(c(80)) = 0: c(80) = 0
800     Next j80

b(c(9)) = 0: c(9) = 0
90      b(c(73)) = 0: c(73) = 0
730     Next j73

b(c(1)) = 0: c(1) = 0
10      b(c(81)) = 0: c(81) = 0
810     Next j81

t2 = Timer

t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem9d2")

End

'   Print results (selected numbers)

1640 For i1 = 1 To 81
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 82).Value = n9
Return

'   Print results (squares)

1650 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 = n9 ''"MC = " + CStr(s1)

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

'   Exclude solutions with identical numbers (Back Check)

1800 fl1 = 1
For j1 = 1 To 81
a2 = a(j1): If a2 = 0 Then GoTo 1810
For j2 = (1 + j1) To 81
If a2 = a(j2) Then fl1 = 0: Return
Next j2
1810 Next j1
Return

End Sub
```