' Generates Composed Magic Squares of order 9 for integers 1 thru 81
' Tested with Office 2007 under Windows 7
Sub MgcSqr9a1()
Dim a(81), b(81), c(81)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr9a1")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 81: s1 = 369
' Generate data
Sheets("Klad1").Select
t1 = Timer
a(41) = 41: b(41) = 41: c(41) = 41
For j81 = 3 To 3 'a(81) = 3
If b(j81) = 0 Then b(j81) = j81: c(81) = j81 Else GoTo 810
a(81) = j81
a(61) = 82 - a(81)
If a(61) <= 0 Or a(61) > 81 Then GoTo 610
If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
For j80 = 16 To 16 'a(80) = 16
If b(j80) = 0 Then b(j80) = j80: c(80) = j80 Else GoTo 800
a(80) = j80
a(60) = 82 - a(80)
If a(60) <= 0 Or a(60) > 81 Then GoTo 600
If b(a(60)) = 0 Then b(a(60)) = a(60): c(60) = a(60) Else GoTo 600
For j79 = 67 To 67 'a(79) = 67
If b(j79) = 0 Then b(j79) = j79: c(79) = j79 Else GoTo 790
a(79) = j79
a(78) = 164 - a(79) - a(80) - a(81)
If a(78) <= 0 Or a(78) > 81 Then GoTo 780
If b(a(78)) = 0 Then b(a(78)) = a(78): c(78) = a(78) Else GoTo 780
a(63) = 82 - a(79)
If a(63) <= 0 Or a(63) > 81 Then GoTo 630
If b(a(63)) = 0 Then b(a(63)) = a(63): c(63) = a(63) Else GoTo 630
a(62) = -82 + a(79) + a(80) + a(81)
If a(62) <= 0 Or a(62) > 81 Then GoTo 620
If b(a(62)) = 0 Then b(a(62)) = a(62): c(62) = a(62) Else GoTo 620
For j72 = 76 To 76 'a(72) = 76
If b(j72) = 0 Then b(j72) = j72: c(72) = j72 Else GoTo 720
a(72) = j72
a(71) = 164 - a(72) - a(80) - a(81)
If a(71) <= 0 Or a(71) > 81 Then GoTo 710
If b(a(71)) = 0 Then b(a(71)) = a(71): c(71) = a(71) Else GoTo 710
a(70) = a(72) - a(79) + a(81)
If a(70) <= 0 Or a(70) > 81 Then GoTo 700
If b(a(70)) = 0 Then b(a(70)) = a(70): c(70) = a(70) Else GoTo 700
a(69) = -a(72) + a(79) + a(80)
If a(69) <= 0 Or a(69) > 81 Then GoTo 690
If b(a(69)) = 0 Then b(a(69)) = a(69): c(69) = a(69) Else GoTo 690
a(54) = 82 - a(72) + a(79) - a(81)
If a(54) <= 0 Or a(54) > 81 Then GoTo 540
If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(53) = 82 + a(72) - a(79) - a(80)
If a(53) <= 0 Or a(53) > 81 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(52) = 82 - a(72)
If a(52) <= 0 Or a(52) > 81 Then GoTo 520
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(51) = -82 + a(72) + a(80) + a(81)
If a(51) <= 0 Or a(51) > 81 Then GoTo 510
If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
For j31 = 29 To 29 'a(31) = 29
If b(j31) = 0 Then b(j31) = j31: c(31) = j31 Else GoTo 310
a(31) = j31
a(11) = 82 - a(31)
If a(11) <= 0 Or a(11) > 81 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j30 = 26 To 26 'a(30) = 26
If b(j30) = 0 Then b(j30) = j30: c(30) = j30 Else GoTo 300
a(30) = j30
a(10) = 82 - a(30)
If a(10) <= 0 Or a(10) > 81 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
For j29 = 55 To 55 'a(29)= 55
If b(j29) = 0 Then b(j29) = j29: c(29) = j29 Else GoTo 290
a(29) = j29
a(28) = 164 - a(29) - a(30) - a(31)
If a(28) <= 0 Or a(28) > 81 Then GoTo 280
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(13) = 82 - a(29)
If a(13) <= 0 Or a(13) > 81 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(12) = -82 + a(29) + a(30) + a(31)
If a(12) <= 0 Or a(12) > 81 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j22 = 46 To 46 'a(22)= 46
If b(j22) = 0 Then b(j22) = j22: c(22) = j22 Else GoTo 220
a(22) = j22
a(21) = 164 - a(22) - a(30) - a(31)
If a(21) <= 0 Or a(21) > 81 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = a(22) - a(29) + a(31)
If a(20) <= 0 Or a(20) > 81 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = -a(22) + a(29) + a(30)
If a(19) <= 0 Or a(19) > 81 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(4) = 82 - a(22) + a(29) - a(31)
If a(4) <= 0 Or a(4) > 81 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = 82 + a(22) - a(29) - a(30)
If a(3) <= 0 Or a(3) > 81 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 82 - a(22)
If a(2) <= 0 Or a(2) > 81 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = -82 + a(22) + a(30) + a(31)
If a(1) <= 0 Or a(1) > 81 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j77 = 80 To 80 'a(77) = 80
If b(j77) = 0 Then b(j77) = j77: c(77) = j77 Else GoTo 770
a(77) = j77
For j76 = 18 To 18 'a(76) = 18
If b(j76) = 0 Then b(j76) = j76: c(76) = j76 Else GoTo 760
a(76) = j76
For j75 = 68 To 68 'a(75) = 68
If b(j75) = 0 Then b(j75) = j75: c(75) = j75 Else GoTo 750
a(75) = j75
For j74 = 38 To 38 'a(74) = 38
If b(j74) = 0 Then b(j74) = j74: c(74) = j74 Else GoTo 740
a(74) = j74
a(73) = 205 - a(74) - a(75) - a(76) - a(77)
If a(73) <= 0 Or a(73) > 81 Then GoTo 730
If b(a(73)) = 0 Then b(a(73)) = a(73): c(73) = a(73) Else GoTo 730
a(68) = -41 + a(74) + a(75)
If a(68) <= 0 Or a(68) > 81 Then GoTo 680
If b(a(68)) = 0 Then b(a(68)) = a(68): c(68) = a(68) Else GoTo 680
For j67 = 37 To 37 'a(67) = 37
If b(j67) = 0 Then b(j67) = j67: c(67) = j67 Else GoTo 670
a(67) = j67
a(56) = -41 + a(67) + a(75)
If a(56) <= 0 Or a(56) > 81 Then GoTo 560
If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(47) = 246 - a(67) - a(74) - a(75) - a(76) - a(77)
If a(47) <= 0 Or a(47) > 81 Then GoTo 470
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(40) = 205 - a(67) - a(75) - a(76) - a(77)
If a(40) <= 0 Or a(40) > 81 Then GoTo 400
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
For j66 = 8 To 8 'a(66) = 8
If b(j66) = 0 Then b(j66) = j66: c(66) = j66 Else GoTo 660
a(66) = j66
a(58) = 246 - a(66) - a(67) - a(74) - a(75) - a(76)
If a(58) <= 0 Or a(58) > 81 Then GoTo 580
If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
a(55) = -205 + a(66) + a(67) + a(74) + a(75) + a(76) + a(77)
If a(55) <= 0 Or a(55) > 81 Then GoTo 550
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(49) = -246 + a(66) + a(67) + a(74) + 2 * a(75) + a(76) + a(77)
If a(49) <= 0 Or a(49) > 81 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(46) = 205 - a(66) - a(67) - a(75) - a(76)
If a(46) <= 0 Or a(46) > 81 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(39) = 205 - a(66) - a(74) - a(75) - a(76)
If a(39) <= 0 Or a(39) > 81 Then GoTo 390
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
For j65 = 81 To 81 'a(65) = 81
If b(j65) = 0 Then b(j65) = j65: c(65) = j65 Else GoTo 650
a(65) = j65
a(64) = 246 - a(65) - a(66) - a(67) - a(74) - a(75)
If a(64) <= 0 Or a(64) > 81 Then GoTo 640
If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640
a(59) = a(65) + a(66) - a(77)
If a(59) <= 0 Or a(59) > 81 Then GoTo 590
If b(a(59)) = 0 Then b(a(59)) = a(59): c(59) = a(59) Else GoTo 590
a(57) = 205 - a(65) - a(66) - a(67) - a(75)
If a(57) <= 0 Or a(57) > 81 Then GoTo 570
If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(50) = 205 - a(65) - a(66) - a(74) - a(75)
If a(50) <= 0 Or a(50) > 81 Then GoTo 500
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(48) = -205 + a(65) + a(66) + a(67) + a(74) + a(75) + a(76)
If a(48) <= 0 Or a(48) > 81 Then GoTo 480
If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(38) = -a(65) + a(76) + a(77)
If a(38) <= 0 Or a(38) > 81 Then GoTo 380
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(37) = -246 + a(65) + a(66) + a(67) + a(74) + 2 * a(75) + a(76)
If a(37) <= 0 Or a(37) > 81 Then GoTo 370
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
For j45 = m1 To m2 'a(45) = 52
If b(j45) = 0 Then b(j45) = j45: c(45) = j45 Else GoTo 450
a(45) = j45
For j44 = m1 To m2 'a(44) = 33
If b(j44) = 0 Then b(j44) = j44: c(44) = j44 Else GoTo 440
a(44) = j44
For j43 = m1 To m2 'a(43) = 57
If b(j43) = 0 Then b(j43) = j43: c(43) = j43 Else GoTo 430
a(43) = j43
a(42) = 164 - a(43) - a(44) - a(45)
If a(42) <= 0 Or a(42) > 81 Then GoTo 420
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
For j36 = m1 To m2 'a(36) = 58
If b(j36) = 0 Then b(j36) = j36: c(36) = j36 Else GoTo 360
a(36) = j36
a(9) = 164 - a(36) - a(44) - a(45)
If a(9) <= 0 Or a(9) > 81 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j35 = m1 To m2 'a(35) = 23
If b(j35) = 0 Then b(j35) = j35: c(35) = j35 Else GoTo 350
a(35) = j35
a(24) = -164 + a(35) + a(36) + a(43) + a(44) + a(45)
If a(24) <= 0 Or a(24) > 81 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(15) = 205 - a(35) - a(36) - a(44) - a(45)
If a(15) <= 0 Or a(15) > 81 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(8) = 205 - a(35) - a(43) - a(44) - a(45)
If a(8) <= 0 Or a(8) > 81 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j34 = m1 To m2 'a(34) = 43
If b(j34) = 0 Then b(j34) = j34: c(34) = j34 Else GoTo 340
a(34) = j34
a(26) = 205 - a(34) - a(35) - a(36) - a(44)
If a(26) <= 0 Or a(26) > 81 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(23) = -41 + a(34) + a(35)
If a(23) <= 0 Or a(23) > 81 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(17) = -205 + a(34) + a(35) + a(36) + a(43) + a(44) + a(45)
If a(17) <= 0 Or a(17) > 81 Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(14) = 205 - a(34) - a(35) - a(43) - a(44)
If a(14) <= 0 Or a(14) > 81 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(7) = 41 - a(34) + a(45)
If a(7) <= 0 Or a(7) > 81 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j33 = m1 To m2 'a(33) = 51
If b(j33) = 0 Then b(j33) = j33: c(33) = j33 Else GoTo 330
a(33) = j33
a(32) = 205 - a(33) - a(34) - a(35) - a(36)
If a(32) <= 0 Or a(32) > 81 Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(27) = a(33) + a(34) - a(45)
If a(27) <= 0 Or a(27) > 81 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(25) = 205 - a(33) - a(34) - a(35) - a(43)
If a(25) <= 0 Or a(25) > 81 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(18) = 41 - a(33) - a(34) + a(44) + a(45)
If a(18) <= 0 Or a(18) > 81 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(16) = -41 + a(33) + a(34) + a(35) - a(45)
If a(16) <= 0 Or a(16) > 81 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(6) = -a(33) + a(44) + a(45)
If a(6) <= 0 Or a(6) > 81 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = -205 + a(33) + a(34) + a(35) + a(36) + a(43) + a(44)
If a(5) <= 0 Or a(5) > 81 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
n9 = n9 + 1
GoSub 2650 'Print results (squares)
' GoSub 2645 'Print results (selected numbers)
b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(16)) = 0: c(16) = 0
160 b(c(18)) = 0: c(18) = 0
180 b(c(25)) = 0: c(25) = 0
250 b(c(27)) = 0: c(27) = 0
270 b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(7)) = 0: c(7) = 0
70 b(c(14)) = 0: c(14) = 0
140 b(c(17)) = 0: c(17) = 0
170 b(c(23)) = 0: c(23) = 0
230 b(c(26)) = 0: c(26) = 0
260 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(8)) = 0: c(8) = 0
80 b(c(15)) = 0: c(15) = 0
150 b(c(24)) = 0: c(24) = 0
240 b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(9)) = 0: c(9) = 0
90 b(c(36)) = 0: c(36) = 0
360 Next j36
b(c(42)) = 0: c(42) = 0
420 b(c(43)) = 0: c(43) = 0
430 Next j43
b(c(44)) = 0: c(44) = 0
440 Next j44
b(c(45)) = 0: c(45) = 0
450 Next j45
b(c(37)) = 0: c(37) = 0
370 b(c(38)) = 0: c(38) = 0
380 b(c(48)) = 0: c(48) = 0
480 b(c(50)) = 0: c(50) = 0
500 b(c(57)) = 0: c(57) = 0
570 b(c(59)) = 0: c(59) = 0
590 b(c(64)) = 0: c(64) = 0
640 b(c(65)) = 0: c(65) = 0
650 Next j65
b(c(39)) = 0: c(39) = 0
390 b(c(46)) = 0: c(46) = 0
460 b(c(49)) = 0: c(49) = 0
490 b(c(55)) = 0: c(55) = 0
550 b(c(58)) = 0: c(58) = 0
580 b(c(66)) = 0: c(66) = 0
660 Next j66
b(c(40)) = 0: c(40) = 0
400 b(c(47)) = 0: c(47) = 0
470 b(c(56)) = 0: c(56) = 0
560 b(c(67)) = 0: c(67) = 0
670 Next j67
b(c(68)) = 0: c(68) = 0
680 b(c(73)) = 0: c(73) = 0
730 b(c(74)) = 0: c(74) = 0
740 Next j74
b(c(75)) = 0: c(75) = 0
750 Next j75
b(c(76)) = 0: c(76) = 0
760 Next j76
b(c(77)) = 0: c(77) = 0
770 Next j77
b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(12)) = 0: c(12) = 0
120 b(c(13)) = 0: c(13) = 0
130 b(c(28)) = 0: c(28) = 0
280 b(c(29)) = 0: c(29) = 0
290 Next j29
b(c(10)) = 0: c(10) = 0
100 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(11)) = 0: c(11) = 0
110 b(c(31)) = 0: c(31) = 0
310 Next j31
b(c(51)) = 0: c(51) = 0
510 b(c(52)) = 0: c(52) = 0
520 b(c(53)) = 0: c(53) = 0
530 b(c(54)) = 0: c(54) = 0
540 b(c(69)) = 0: c(69) = 0
690 b(c(70)) = 0: c(70) = 0
700 b(c(71)) = 0: c(71) = 0
710 b(c(72)) = 0: c(72) = 0
720 Next j72
b(c(62)) = 0: c(62) = 0
620 b(c(63)) = 0: c(63) = 0
630 b(c(78)) = 0: c(78) = 0
780 b(c(79)) = 0: c(79) = 0
790 Next j79
b(c(60)) = 0: c(60) = 0
600 b(c(80)) = 0: c(80) = 0
800 Next j80
b(c(61)) = 0: c(61) = 0
610 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 MgcSqr9a1")
End
' Print results (selected numbers)
2645 For i1 = 1 To 81
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
2650 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
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
End Sub
