' Generates Concentric Magic Squares of order 9 with 4 x 3 Even Corner Numbers
' Suitable for Concentric Lozenge Squares of order 13 (Predefined Border)
' Tested with Office 2007 under Windows 7
Sub Priem9c1()
Dim a1(121), a(81), a7(49), b(167), b1(167), c(81)
y = MsgBox("Locked", vbCritical, "Routine Priem9c")
End
n5 = 0: n9 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 49 ''365
' Define Variables
a1(1) = 3: a1(2) = 4: a1(3) = 5: a1(4) = 6: a1(5) = 7:
a1(6) = 8: a1(7) = 9: a1(8) = 10: a1(9) = 11:
a1(10) = 15: a1(11) = 17: a1(12) = 18: a1(13) = 19: a1(14) = 20:
a1(15) = 21: a1(16) = 22: a1(17) = 23: a1(18) = 25:
a1(19) = 27: a1(20) = 29: a1(21) = 31: a1(22) = 32: a1(23) = 33:
a1(24) = 34: a1(25) = 35: a1(26) = 37: a1(27) = 39:
a1(28) = 40: a1(29) = 41: a1(30) = 43: a1(31) = 45: a1(32) = 46:
a1(33) = 47: a1(34) = 49: a1(35) = 51: a1(36) = 52:
a1(37) = 53: a1(38) = 54: a1(39) = 55: a1(40) = 57: a1(41) = 59:
a1(42) = 61: a1(43) = 63: a1(44) = 64: a1(45) = 65:
a1(46) = 66: a1(47) = 67: a1(48) = 68: a1(49) = 69: a1(50) = 71:
a1(51) = 73: a1(52) = 75: a1(53) = 76: a1(54) = 77:
a1(55) = 78: a1(56) = 79: a1(57) = 80: a1(58) = 81: a1(59) = 82:
a1(60) = 83: a1(61) = 85: a1(62) = 87: a1(63) = 88:
a1(64) = 89: a1(65) = 90: a1(66) = 91: a1(67) = 92: a1(68) = 93:
a1(69) = 94: a1(70) = 95: a1(71) = 97: a1(72) = 99:
a1(73) = 101: a1(74) = 102: a1(75) = 103: a1(76) = 104: a1(77) = 105:
a1(78) = 106: a1(79) = 107: a1(80) = 109: a1(81) = 111:
a1(82) = 113: a1(83) = 115: a1(84) = 116: a1(85) = 117: a1(86) = 118:
a1(87) = 119: a1(88) = 121: a1(89) = 123: a1(90) = 124:
a1(91) = 125: a1(92) = 127: a1(93) = 129: a1(94) = 130: a1(95) = 131:
a1(96) = 133: a1(97) = 135: a1(98) = 136: a1(99) = 137:
a1(100) = 138: a1(101) = 139: a1(102) = 141: a1(103) = 143: a1(104) = 145:
a1(105) = 147: a1(106) = 148: a1(107) = 149: a1(108) = 150:
a1(109) = 151: a1(110) = 152: a1(111) = 153: a1(112) = 155: a1(113) = 159:
a1(114) = 160: a1(115) = 161: a1(116) = 162: a1(117) = 163:
a1(118) = 164: a1(119) = 165: a1(120) = 166: a1(121) = 167:
s1 = 765: p2 = 170: 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 = m1 To m2 'a(80) even
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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 'a(74) even
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 = m1 To m2 'a(72) even
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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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 = m1 To m2 '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) even
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 Priem9c")
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 = 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
