' Generates Inlaid Magic Squares of order 9 (Integers 1 ... 81)
' Tested with Office 2007 under Windows 7
Sub MgcSqr9k()
Dim a1(81), a(81), b1(81), b(81), c(81), s(4)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr9k")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 81: s9 = 369: Pr9 = 82
For i1 = 1 To m2
a1(i1) = i1
b1(a1(i1)) = a1(i1)
Next i1
Sheets("Klad1").Select
t1 = Timer
For s3 = 99 To 114 Step 3
s(3) = s3
For s4 = 174 To 194 Step 2
s(4) = s4
s(1) = 8 * s9 / 9 - s(4)
s(2) = 6 * s9 / 9 - s(3)
' Generate Squares (3 x 3)
t11 = Timer 'Time Out
a(41) = 41: b(41) = 41 'Define Center Element
For j67 = m1 To m2' 'a(67)
If b(a1(j67)) = 0 Then b(a1(j67)) = a1(j67): c(67) = a1(j67) Else GoTo 670
a(67) = a1(j67)
a(15) = Pr9 - a(67): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j66 = m1 To m2' 'a(66)
If b(a1(j66)) = 0 Then b(a1(j66)) = a1(j66): c(66) = a1(j66) Else GoTo 660
a(66) = a1(j66)
a(16) = Pr9 - a(66): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(65) = s(3) - a(66) - a(67):
If a(65) < a1(m1) Or a(65) > a1(m2) Then GoTo 650:
If b1(a(65)) = 0 Then GoTo 650
If b(a(65)) = 0 Then b(a(65)) = a(65): c(65) = a(65) Else GoTo 650
a(17) = Pr9 - a(65): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(58) = 4 * s(3) / 3 - a(66) - 2 * a(67):
If a(58) < a1(m1) Or a(58) > a1(m2) Then GoTo 580:
If b1(a(58)) = 0 Then GoTo 580
If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
a(24) = Pr9 - a(58): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(57) = s(3) / 3:
If a(57) < a1(m1) Or a(57) > a1(m2) Then GoTo 570:
If b1(a(57)) = 0 Then GoTo 570
If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(25) = Pr9 - a(57): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(56) = -2 * s(3) / 3 + a(66) + 2 * a(67):
If a(56) < a1(m1) Or a(56) > a1(m2) Then GoTo 560:
If b1(a(56)) = 0 Then GoTo 560
If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(26) = Pr9 - a(56): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(49) = -s(3) / 3 + a(66) + a(67):
If a(49) < a1(m1) Or a(49) > a1(m2) Then GoTo 490:
If b1(a(49)) = 0 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(33) = Pr9 - a(49): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(48) = 2 * s(3) / 3 - a(66):
If a(48) < a1(m1) Or a(48) > a1(m2) Then GoTo 480:
If b1(a(48)) = 0 Then GoTo 480
If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(34) = Pr9 - a(48): If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(47) = 2 * s(3) / 3 - a(67):
If a(47) < a1(m1) Or a(47) > a1(m2) Then GoTo 470:
If b1(a(47)) = 0 Then GoTo 470
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(35) = Pr9 - a(47): If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
' Center squares (4 x 4)
For j42 = m1 To m2' 'a(42)
If b(a1(j42)) = 0 Then b(a1(j42)) = a1(j42): c(42) = a1(j42) Else GoTo 420
a(42) = a1(j42)
a(40) = Pr9 - a(42): If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
For j43 = m1 To m2' 'a(43)
If b(a1(j43)) = 0 Then b(a1(j43)) = a1(j43): c(43) = a1(j43) Else GoTo 430
a(43) = a1(j43)
a(39) = Pr9 - a(43): If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(44) = s(4) - a(43) - a(42) - a(41)
If a(44) < a1(m1) Or a(44) > a1(m2) Then GoTo 440
If b1(a(44)) = 0 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(38) = Pr9 - a(44): If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
For j50 = m1 To m2' 'a(50)
If b(a1(j50)) = 0 Then b(a1(j50)) = a1(j50): c(50) = a1(j50) Else GoTo 500
a(50) = a1(j50)
a(32) = Pr9 - a(50): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
For j51 = m1 To m2' 'a(51)
If b(a1(j51)) = 0 Then b(a1(j51)) = a1(j51): c(51) = a1(j51) Else GoTo 552
a(51) = a1(j51)
a(31) = Pr9 - a(51): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
For j52 = m1 To m2' 'a(52)
If b(a1(j52)) = 0 Then b(a1(j52)) = a1(j52): c(52) = a1(j52) Else GoTo 520
a(52) = a1(j52)
a(30) = Pr9 - a(52): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(53) = s(4) - a(52) - a(51) - a(50)
If a(53) < a1(m1) Or a(53) > a1(m2) Then GoTo 530
If b1(a(53)) = 0 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(29) = Pr9 - a(53): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
For j59 = m1 To m2' 'a(59)
If b(a1(j59)) = 0 Then b(a1(j59)) = a1(j59): c(59) = a1(j59) Else GoTo 590
a(59) = a1(j59)
a(23) = Pr9 - a(59): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(60) = a(59) - a(52) + a(50) - a(44) + a(41)
If a(60) < a1(m1) Or a(60) > a1(m2) Then GoTo 600:
If b1(a(60)) = 0 Then GoTo 600
If b(a(60)) = 0 Then b(a(60)) = a(60): c(60) = a(60) Else GoTo 600
a(22) = Pr9 - a(60): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(61) = s(4) - a(59) - a(51) - a(50) + a(44) - a(41)
If a(61) < a1(m1) Or a(61) > a1(m2) Then GoTo 610:
If b1(a(61)) = 0 Then GoTo 610
If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
a(21) = Pr9 - a(61): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(62) = -a(59) + a(52) + a(51)
If a(62) < a1(m1) Or a(62) > a1(m2) Then GoTo 620:
If b1(a(62)) = 0 Then GoTo 620
If b(a(62)) = 0 Then b(a(62)) = a(62): c(62) = a(62) Else GoTo 620
a(20) = Pr9 - a(62): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(68) = s(4) - a(60) - a(52) - a(44)
If a(68) < a1(m1) Or a(68) > a1(m2) Then GoTo 680:
If b1(a(68)) = 0 Then GoTo 680
If b(a(68)) = 0 Then b(a(68)) = a(68): c(68) = a(68) Else GoTo 680
a(14) = Pr9 - a(68): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(69) = -s(4) - a(59) + a(53) + 2 * a(52) + 2 * a(44) + a(43)
If a(69) < a1(m1) Or a(69) > a1(m2) Then GoTo 690:
If b1(a(69)) = 0 Then GoTo 690
If b(a(69)) = 0 Then b(a(69)) = a(69): c(69) = a(69) Else GoTo 690
a(13) = Pr9 - a(69): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(70) = a(59) - a(53) - 2 * a(52) + a(42) + 2 * a(41)
If a(70) < a1(m1) Or a(70) > a1(m2) Then GoTo 700:
If b1(a(70)) = 0 Then GoTo 700
If b(a(70)) = 0 Then b(a(70)) = a(70): c(70) = a(70) Else GoTo 700
a(12) = Pr9 - a(70): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(71) = a(59) + a(50) - a(44)
If a(71) < a1(m1) Or a(71) > a1(m2) Then GoTo 710:
If b1(a(71)) = 0 Then GoTo 710
If b(a(71)) = 0 Then b(a(71)) = a(71): c(71) = a(71) Else GoTo 710
a(11) = Pr9 - a(71): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
n10 = n10 + 1: Cells(k1, 1).Select: Cells(k1, 1).Value = n10
t12 = Timer: t13 = t12 - t11 'Time Out
If t13 > 10 Then Erase b, c: GoTo 1000 'Time Out, Try Next
' Create Border
For j81 = m1 To m2 '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) = Pr9 - 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)
If b(a1(j80)) = 0 Then b(a1(j80)) = a1(j80): c(80) = a1(j80) Else GoTo 800
a(80) = a1(j80)
a(74) = -s9 / 9 + a(80) - s(3) + s(4)
If a(74) < a1(m1) Or a(74) > a1(m2) Then GoTo 740
If b1(a(74)) = 0 Then GoTo 740
If b(a(74)) = 0 Then b(a(74)) = a(74): c(74) = a(74) Else GoTo 740
a(8) = Pr9 - a(74): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(2) = Pr9 - a(80): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j79 = m1 To m2 '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(75) = -s9 / 9 + a(79) - s(3) + s(4)
If a(75) < a1(m1) Or a(75) > a1(m2) Then GoTo 750
If b1(a(75)) = 0 Then GoTo 750
If b(a(75)) = 0 Then b(a(75)) = a(75): c(75) = a(75) Else GoTo 750
a(7) = Pr9 - a(75): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(3) = Pr9 - a(79): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j78 = m1 To m2 '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(76) = -s9 / 9 + a(78) - s(3) + s(4)
If a(76) < a1(m1) Or a(76) > a1(m2) Then GoTo 760
If b1(a(76)) = 0 Then GoTo 760
If b(a(76)) = 0 Then b(a(76)) = a(76): c(76) = a(76) Else GoTo 760
a(6) = Pr9 - a(76): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(4) = Pr9 - a(78): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j77 = m1 To m2 '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(73) = 12 * s9 / 9 - a(77) - 2 * a(78) - 2 * a(79) - 2 * a(80) - a(81) + 3 * s(3) - 3 * s(4)
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) = Pr9 - a(73): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(5) = Pr9 - a(77): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j72 = m1 To m2 '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) = s9 - a(72) - s(3) - s(4)
If a(64) < a1(m1) Or a(64) > a1(m2) Then GoTo 640
If b1(a(64)) = 0 Then GoTo 640
If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640
a(18) = Pr9 - a(64): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(10) = Pr9 - a(72): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
For j63 = m1 To m2 '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) = s9 - a(63) - s(3) - s(4)
If a(55) < a1(m1) Or a(55) > a1(m2) Then GoTo 550
If b1(a(55)) = 0 Then GoTo 550
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(27) = Pr9 - a(55): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(19) = Pr9 - a(63): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
For j54 = m1 To m2 '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) = s9 - a(54) - s(3) - s(4)
If a(46) < a1(m1) Or a(46) > a1(m2) Then GoTo 460
If b1(a(46)) = 0 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(45) = 40 * s9 / 9 - 2*a(54) - 2*a(63) - 2*a(72) - a(77) - 2*a(78) - 2*a(79) - 2*a(80) - 2*a(81) - 6*s(4)
If a(45) < a1(m1) Or a(45) > a1(m2) Then GoTo 450
If b1(a(45)) = 0 Then GoTo 450
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(37) = Pr9 - a(45): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(36) = Pr9 - a(46): If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(28) = Pr9 - a(54): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
GoSub 1300: If fl1 = 0 Then GoTo 5 'Back Check Identical Numbers
n9 = n9 + 1: GoSub 1500 'Print Square
Erase b, c: GoTo 1000 'Print only one square
5
b(c(28)) = 0: c(28) = 0
280 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 b(c(45)) = 0: c(45) = 0
450 b(c(46)) = 0: c(46) = 0
460 b(c(54)) = 0: c(54) = 0
540 Next j54
b(c(19)) = 0: c(19) = 0
190 b(c(27)) = 0: c(27) = 0
270 b(c(55)) = 0: c(55) = 0
550 b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(10)) = 0: c(10) = 0
100 b(c(18)) = 0: c(18) = 0
180 b(c(64)) = 0: c(64) = 0
640 b(c(72)) = 0: c(72) = 0
720 Next j72
b(c(5)) = 0: c(5) = 0
50 b(c(9)) = 0: c(9) = 0
90 b(c(73)) = 0: c(73) = 0
730 b(c(77)) = 0: c(77) = 0
770 Next j77
b(c(4)) = 0: c(4) = 0
40 b(c(6)) = 0: c(6) = 0
60 b(c(76)) = 0: c(76) = 0
760 b(c(78)) = 0: c(78) = 0
780 Next j78
b(c(3)) = 0: c(3) = 0
30 b(c(7)) = 0: c(7) = 0
70 b(c(75)) = 0: c(75) = 0
750 b(c(79)) = 0: c(79) = 0
790 Next j79
b(c(2)) = 0: c(2) = 0
20 b(c(8)) = 0: c(8) = 0
80 b(c(74)) = 0: c(74) = 0
740 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
' End Border
b(c(11)) = 0: c(11) = 0
110 b(c(71)) = 0: c(71) = 0
710 b(c(12)) = 0: c(12) = 0
120 b(c(70)) = 0: c(70) = 0
700 b(c(13)) = 0: c(13) = 0
130 b(c(69)) = 0: c(69) = 0
690 b(c(14)) = 0: c(14) = 0
140 b(c(68)) = 0: c(68) = 0
680 b(c(20)) = 0: c(20) = 0
200 b(c(62)) = 0: c(62) = 0
620 b(c(21)) = 0: c(21) = 0
210 b(c(61)) = 0: c(61) = 0
610 b(c(22)) = 0: c(22) = 0
220 b(c(60)) = 0: c(60) = 0
600 b(c(23)) = 0: c(23) = 0
230 b(c(59)) = 0: c(59) = 0
590 Next j59
b(c(29)) = 0: c(29) = 0
290 b(c(53)) = 0: c(53) = 0
530 b(c(30)) = 0: c(30) = 0
300 b(c(52)) = 0: c(52) = 0
520 Next j52
b(c(31)) = 0: c(31) = 0
310 b(c(51)) = 0: c(51) = 0
552 Next j51
b(c(32)) = 0: c(32) = 0
320 b(c(50)) = 0: c(50) = 0
500 Next j50
b(c(38)) = 0: c(38) = 0
380 b(c(44)) = 0: c(44) = 0
440 b(c(39)) = 0: c(39) = 0
390 b(c(43)) = 0: c(43) = 0
430 Next j43
b(c(40)) = 0: c(40) = 0
400 b(c(42)) = 0: c(42) = 0
420 Next j42
' End Center Squares (4 x 4)
b(c(35)) = 0: c(35) = 0
350 b(c(47)) = 0: c(47) = 0
470 b(c(34)) = 0: c(34) = 0
340 b(c(48)) = 0: c(48) = 0
480 b(c(33)) = 0: c(33) = 0
330 b(c(49)) = 0: c(49) = 0
490 b(c(26)) = 0: c(26) = 0
260 b(c(56)) = 0: c(56) = 0
560 b(c(25)) = 0: c(25) = 0
250 b(c(57)) = 0: c(57) = 0
570 b(c(24)) = 0: c(24) = 0
240 b(c(58)) = 0: c(58) = 0
580 b(c(17)) = 0: c(17) = 0
170 b(c(65)) = 0: c(65) = 0
650 b(c(16)) = 0: c(16) = 0
160 b(c(66)) = 0: c(66) = 0
660 Next j66
b(c(15)) = 0: c(15) = 0
150 b(c(67)) = 0: c(67) = 0
670 Next j67
1000
Next s4
Next s3
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine MgcSqr9k")
End
' Print results (squares)
1500 n2 = n2 + 1
If n2 = 3 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
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
1300 fl1 = 1
For j10 = 1 To 81
c2 = a(j10): If c2 = 0 Then GoTo 1310
For j20 = (1 + j10) To 81
If c2 = a(j20) Then fl1 = 0: Return
Next j20
1310 Next j10
Return
End Sub
