' 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
Sheets("Klad1").Select
' 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
