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' Generates Concentric Magic Squares of order 9 with 4 Even Corner Numbers
' Suitable for Concentric Lozenge Squares of order 15 (Predefined Borders)

' Tested with Office 2007 under Windows 7

```Sub Priem9c2()

Dim a1(121), a(81), a7(49), b(221), b1(221), c(81)

y = MsgBox("Locked", vbCritical, "Routine Priem9c2")
End

n5 = 0: n9 = 0: k1 = 1: k2 = 1

Sheets("Klad1").Select

t1 = Timer

For j100 = 1 To 48

'   Define Variables

a1(1) = 5: a1(2) = 6: a1(3) = 7: a1(4) = 8: a1(5) = 9: a1(6) = 10:
a1(7) = 11: a1(8) = 19: a1(9) = 21: a1(10) = 22:
a1(11) = 23: a1(12) = 24: a1(13) = 25: a1(14) = 27: a1(15) = 33:
a1(16) = 35: a1(17) = 37: a1(18) = 38: a1(19) = 39:
a1(20) = 41: a1(21) = 43: a1(22) = 47: a1(23) = 49: a1(24) = 51:
a1(25) = 53: a1(26) = 55: a1(27) = 57: a1(28) = 59:
a1(29) = 61: a1(30) = 63: a1(31) = 65: a1(32) = 67: a1(33) = 69:
a1(34) = 71: a1(35) = 73: a1(36) = 74: a1(37) = 75:
a1(38) = 76: a1(39) = 77: a1(40) = 79: a1(41) = 81: a1(42) = 83:
a1(43) = 85: a1(44) = 87: a1(45) = 89: a1(46) = 91:
a1(47) = 92: a1(48) = 93: a1(49) = 94: a1(50) = 95: a1(51) = 97:
a1(52) = 99: a1(53) = 101: a1(54) = 103: a1(55) = 105:
a1(56) = 106: a1(57) = 107: a1(58) = 108: a1(59) = 109: a1(60) = 111:
a1(61) = 113: a1(62) = 115: a1(63) = 117: a1(64) = 118:
a1(65) = 119: a1(66) = 120: a1(67) = 121: a1(68) = 123: a1(69) = 125:
a1(70) = 127: a1(71) = 129: a1(72) = 131: a1(73) = 132:
a1(74) = 133: a1(75) = 134: a1(76) = 135: a1(77) = 137: a1(78) = 139:
a1(79) = 141: a1(80) = 143: a1(81) = 145: a1(82) = 147:
a1(83) = 149: a1(84) = 150: a1(85) = 151: a1(86) = 152: a1(87) = 153:
a1(88) = 155: a1(89) = 157: a1(90) = 159: a1(91) = 161:
a1(92) = 163: a1(93) = 165: a1(94) = 167: a1(95) = 169: a1(96) = 171:
a1(97) = 173: a1(98) = 175: a1(99) = 177: a1(100) = 179:
a1(101) = 183: a1(102) = 185: a1(103) = 187: a1(104) = 188: a1(105) = 189:
a1(106) = 191: a1(107) = 193: a1(108) = 199: a1(109) = 201:
a1(110) = 202: a1(111) = 203: a1(112) = 204: a1(113) = 205: a1(114) = 207:
a1(115) = 215: a1(116) = 216: a1(117) = 217: a1(118) = 218:
a1(119) = 219: a1(120) = 220: a1(121) = 221:

s1 = 1017: p2 = 226: m1 = 1: m2 = 121
aMin = a1(1): aMax = a1(121)

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

'   Read Center Square

For i1 = 1 To 49
a7(i1) = Sheets("Center7").Cells(j100, i1):  b1(a7(i1)) = 0
Next i1

'   Reduce Variables

i2 = 0
For i1 = aMin To aMax
If b1(i1) = i1 Then
i2 = i2 + 1: a1(i2) = i1
End If
Next i1
m2 = i2

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

'   Store Center Square in a()

Erase a
a(11) = a7(1):  a(12) = a7(2):  a(13) = a7(3):  a(14) = a7(4):  a(15) = a7(5):  a(16) = a7(6):  a(17) = a7(7):
a(20) = a7(8):  a(21) = a7(9):  a(22) = a7(10): a(23) = a7(11): a(24) = a7(12): a(25) = a7(13): a(26) = a7(14):
a(29) = a7(15): a(30) = a7(16): a(31) = a7(17): a(32) = a7(18): a(33) = a7(19): a(34) = a7(20): a(35) = a7(21):
a(38) = a7(22): a(39) = a7(23): a(40) = a7(24): a(41) = a7(25): a(42) = a7(26): a(43) = a7(27): a(44) = a7(28):
a(47) = a7(29): a(48) = a7(30): a(49) = a7(31): a(50) = a7(32): a(51) = a7(33): a(52) = a7(34): a(53) = a7(35):
a(56) = a7(36): a(57) = a7(37): a(58) = a7(38): a(59) = a7(39): a(60) = a7(40): a(61) = a7(41): a(62) = a7(42):
a(65) = a7(43): a(66) = a7(44): a(67) = a7(45): a(68) = a7(46): a(69) = a7(47): a(70) = a7(48): a(71) = a7(49):

'   Determine Border(s)

For j81 = m1 To m2                                                    'a(81) even
If CInt(a1(j81) / 2) <> a1(j81) / 2 Then GoTo 810
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 j80 = m2 To m1 Step -1                                          'a(80) odd
If CInt(a1(j80) / 2) = a1(j80) / 2 Then GoTo 800
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)odd
If CInt(a1(j79) / 2) = a1(j79) / 2 Then GoTo 790
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)odd
If CInt(a1(j78) / 2) = a1(j78) / 2 Then GoTo 780
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) odd
If CInt(a1(j77) / 2) = a1(j77) / 2 Then GoTo 770
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) odd
If CInt(a1(j76) / 2) = a1(j76) / 2 Then GoTo 760
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) odd
If CInt(a1(j75) / 2) = a1(j75) / 2 Then GoTo 750
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

For j74 = j75 - 1 To m1 Step -1                                          'a(74) odd
If CInt(a1(j74) / 2) = a1(j74) / 2 Then GoTo 740
If b(a1(j74)) = 0 Then b(a1(j74)) = a1(j74): c(74) = a1(j74) Else GoTo 740
a(74) = a1(j74)

a(73) = s1 - a(74) - a(75) - a(76) - a(77) - a(78) - a(79) - a(80) - a(81)
If CInt(a(73) / 2) <> a(73) / 2 Then GoTo 730                         'a(73) even
If a(73) < a1(m1) Or a(73) > a1(m2) Then GoTo 730
If b1(a(73)) = 0 Then GoTo 730
If b(a(73)) = 0 Then b(a(73)) = a(73): c(73) = a(73) Else GoTo 730

a(9) = p2 - a(73): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
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) odd
If CInt(a1(j72) / 2) = a1(j72) / 2 Then GoTo 720
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) odd
If CInt(a1(j63) / 2) = a1(j63) / 2 Then GoTo 630
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) odd
If CInt(a1(j54) / 2) = a1(j54) / 2 Then GoTo 540
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) odd
If CInt(a1(j45) / 2) = a1(j45) / 2 Then GoTo 450
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) odd
If CInt(a1(j36) / 2) = a1(j36) / 2 Then GoTo 360
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) odd
If CInt(a1(j27) / 2) = a1(j27) / 2 Then GoTo 270
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) = 7 * p2 / 2 - a(27) - a(36) - a(45) - a(54) - a(63) - a(72) + a(73) - a(81)
If CInt(a(18) / 2) = a(18) / 2 Then GoTo 180                          'a(18) odd
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(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

GoSub 1800: If fl1 = 0 Then GoTo 5

n9 = n9 + 1
'                               GoSub 2650              'Print results (squares)
GoSub 2645              'Print results (selected numbers)

Erase b, c: GoTo 1000   'Print only first square

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(9)) = 0: c(9) = 0
90      b(c(73)) = 0: c(73) = 0
730     b(c(74)) = 0: c(74) = 0
740     Next j74
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(1)) = 0: c(1) = 0
10      b(c(81)) = 0: c(81) = 0
810     Next j81

Erase b, c
1000 Next j100

t2 = Timer

t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem9c2")

End

'   Print results (selected numbers)

2645 For i1 = 1 To 81
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 82).Value = n9
Cells(n9, 82).Select
Return

'   Print results (squares)

2650 n5 = n5 + 1
If n5 = 4 Then
n5 = 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 = s1 ''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

'   Exclude solutions with identical numbers

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
```

 About the Author