' Generates Four Way Bent Diagonal Ultr Magic Squares of order 9 (MC = 369)
' Tested with Office 365 under Windows 10
Sub BentDia94()
Dim a(81), b(81), c(81), m(81)
y = MsgBox("Locked", vbCritical, "Routine BentDia94")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 81: s1 = 369: p2 = 82
' Generate data
Sheets("Klad1").Select
t1 = Timer
a(41) = 41: b(41) = 41: c(41) = 41
For j81 = m1 To m2 'a(81)
If b(j81) = 0 Then b(j81) = j81: c(81) = j81 Else GoTo 810
a(81) = 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)
If b(j80) = 0 Then b(j80) = j80: c(80) = j80 Else GoTo 800
a(80) = j80
a(2) = p2 - 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(j79) = 0 Then b(j79) = j79: c(79) = j79 Else GoTo 790
a(79) = j79
a(3) = p2 - 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(j78) = 0 Then b(j78) = j78: c(78) = j78 Else GoTo 780
a(78) = j78
a(4) = p2 - 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(j77) = 0 Then b(j77) = j77: c(77) = j77 Else GoTo 770
a(77) = 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)
If b(j76) = 0 Then b(j76) = j76: c(76) = j76 Else GoTo 760
a(76) = j76
a(6) = p2 - a(76): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j75 = m1 To m2 'a(75)
If b(j75) = 0 Then b(j75) = j75: c(75) = j75 Else GoTo 750
a(75) = j75
a(7) = p2 - a(75): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j74 = m1 To m2 'a(74)
If b(j74) = 0 Then b(j74) = j74: c(74) = j74 Else GoTo 740
a(74) = j74
a(73) = s1 - a(74) - a(75) - a(76) - a(77) - a(78) - a(79) - a(80) - a(81)
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) = -4*s1/9 + a(74) + a(75) + a(77) + a(79) + a(80)
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
a(14) = p2 - a(68): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(9) = p2 - a(73): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = p2 - a(74): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j72 = m1 To m2 'a(72)
If b(j72) = 0 Then b(j72) = j72: c(72) = j72 Else GoTo 720
a(72) = j72
a(64) = 5*s1/9 - a(72) - a(74) - a(77) - a(80)
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(45) = 6*s1/9 - 2*a(72) - a(77) - 2*a(80)
If a(45) <= 0 Or a(45) > 81 Then GoTo 450
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(37) = p2 - a(45): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(18) = p2 - a(64): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(10) = p2 - a(72): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
For j71 = m1 To m2 'a(71)
If b(j71) = 0 Then b(j71) = j71: c(71) = j71 Else GoTo 710
a(71) = j71
a(63) = 4*s1/9 - a(71) - a(79) - a(81)
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(19) = p2 - a(63): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(11) = p2 - a(71): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j70 = m1 To m2 'a(70)
If b(j70) = 0 Then b(j70) = j70: c(70) = j70 Else GoTo 700
a(70) = j70
a(12) = p2 - a(70): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j69 = m1 To m2 'a(69)
If b(j69) = 0 Then b(j69) = j69: c(69) = j69 Else GoTo 690
a(69) = j69
a(13) = p2 - a(69): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j67 = m1 To m2 'a(67)
If b(j67) = 0 Then b(j67) = j67: c(67) = j67 Else GoTo 670
a(67) = j67
a(59) = 6*s1/9 - a(67) - a(69) - a(75) - a(77) - a(79)
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(42) = s1/9 + a(67) - a(69) + a(75) + a(76) - a(78) - a(79)
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
a(40) = p2 - a(42): If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(23) = p2 - a(59): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(15) = p2 - 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(j66) = 0 Then b(j66) = j66: c(66) = j66 Else GoTo 660
a(66) = j66
a(65) = 8*s1/9 - a(66) - a(67) - a(69) - a(70) - a(71) - a(75) - a(79)
If a(65) <= 0 Or a(65) > 81 Then GoTo 650
If b(a(65)) = 0 Then b(a(65)) = a(65): c(65) = a(65) Else GoTo 650
a(55) = -13*s1/9 + a(66) + a(67) + a(69) + a(70) + a(71) + a(74) + a(75) + a(76) + a(77) + a(78) +
+ 2*a(79) + a(80) + a(81)
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(44) = 18*s1/9 - a(66) - a(67) - a(69) - a(70) - 2*a(71) - a(75) - a(76) - a(77) - a(78) - 3*a(79) +
- 2*a(80) - 2*a(81)
If a(44) <= 0 Or a(44) > 81 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(43) = s1/9 + a(66) - a(70) + a(74) + a(75) + a(76) - a(78) - a(79) - a(80)
If a(43) <= 0 Or a(43) > 81 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(39) = p2 - a(43): If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(38) = p2 - a(44): If b(a(38)) = 0 Then b(a(38)) = a(39): c(38) = a(38) Else GoTo 380
a(27) = p2 - a(55): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(17) = p2 - a(65): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(16) = p2 - a(66): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j62 = m1 To m2 'a(62)
If b(j62) = 0 Then b(j62) = j62: c(62) = j62 Else GoTo 620
a(62) = j62
a(56) = -13*s1/9 + a(62) + a(67) + a(69) + 2*a(70) + 2*a(71) + 2*a(72) - a(74) - a(76) + a(77) +
+ a(78) + 2*a(79) + 3*a(80)
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(54) = 6*s1/9 - a(62) - a(70) - a(72) - a(78) - a(80)
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(46) = 14*s1/9 - a(62) - a(66) - a(67) - a(69) - 2*a(70) - 2*a(71) - a(72) + a(74) - a(78) - 2*a(79) - 2*a(80)
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(36) = p2 - a(46): If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(28) = p2 - a(54): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(26) = p2 - a(56): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(20) = p2 - a(62): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
For j61 = m1 To m2 'a(61)
If b(j61) = 0 Then b(j61) = j61: c(61) = j61 Else GoTo 610
a(61) = j61
a(60) = 21*s1/9 - a(61) - a(62) - 2*a(69) - 3*a(70) - 2*a(71) - a(72) + 0.5*a(74) + 0.5*a(75) + 0.5*a(76) +
- a(77) - 2.5*a(78) - 3.5*a(79) - 3.5*a(80) - a(81)
If a(60) <= 0 Or a(60) > 81 Or CInt(a(60)) <> a(60) Then GoTo 600
If b(a(60)) = 0 Then b(a(60)) = a(60): c(60) = a(60) Else GoTo 600
a(58) = a(60) - a(66) - a(67) + a(69) + a(70) - a(74) - a(75) - a(76) + a(78) + a(79) + a(80)
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(57) = -17*s1/9 + a(61) + 2*a(69) + 2*a(70) + 2*a(71) + a(77) + 2*a(78) + 4*a(79) + 2*a(80) + 2*a(81)
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(53) = s1/9 - a(61) - a(69) + a(72) + 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) = -16*s1/9 + a(61) + 2*a(69) + 2*a(70) + 2*a(71) - 0.5*a(74) - 0.5*a(75) - 0.5*a(76) + a(77) +
+ 2.5*a(78) + 3.5*a(79) + 2.5*a(80) + 2*a(81)
If a(52) <= 0 Or a(52) > 81 Or CInt(a(52)) <> a(52) Then GoTo 520
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(51) = 4*s1/9 - a(61) - a(71) - 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
a(50) = -28*s1/9 + 2*a(61) + 2*a(62) + a(67) + 3*a(69) + 4*a(70) + 4*a(71) + 2*a(72) - 2*a(74) +
- a(75) - a(76) + a(77) + 3*a(78) + 5*a(79) + 4*a(80) + 2*a(81)
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(49) = 4*s1/9 - a(57) - a(65) - a(73)
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(48) = (2*s1/9 + 2*a(61) + a(74) - a(75) + a(76) - a(78) - a(79) - a(80)) / 2
If a(48) <= 0 Or a(48) > 81 Or CInt(a(48)) <> a(48) Then GoTo 480
If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(47) = 23*s1/9 - a(61) - a(67) - 2*a(69) - 2*a(70) - 2*a(71) - a(72) - 2*a(77) - 2*a(78) +
- 4*a(79) - 3*a(80) - 2*a(81)
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(35) = p2 - a(47): If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(34) = p2 - a(48): If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(33) = p2 - a(49): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(32) = p2 - a(50): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(31) = p2 - a(51): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(30) = p2 - a(52): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(29) = p2 - a(53): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(25) = p2 - a(57): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(24) = p2 - a(58): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(22) = p2 - a(60): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = p2 - a(61): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
n9 = n9 + 1
GoSub 2650 'Print results (squares)
' GoSub 2645 'Print results (selected numbers
b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 b(c(24)) = 0: c(24) = 0
240 b(c(25)) = 0: c(25) = 0
250 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 b(c(34)) = 0: c(34) = 0
340 b(c(35)) = 0: c(35) = 0
350 b(c(47)) = 0: c(47) = 0
470 b(c(48)) = 0: c(48) = 0
480 b(c(49)) = 0: c(49) = 0
490 b(c(50)) = 0: c(50) = 0
500 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(57)) = 0: c(57) = 0
570 b(c(58)) = 0: c(58) = 0
580 b(c(60)) = 0: c(60) = 0
600 b(c(61)) = 0: c(61) = 0
610 Next j61
b(c(20)) = 0: c(20) = 0
200 b(c(26)) = 0: c(26) = 0
260 b(c(28)) = 0: c(28) = 0
280 b(c(36)) = 0: c(36) = 0
360 b(c(46)) = 0: c(46) = 0
460 b(c(54)) = 0: c(54) = 0
540 b(c(56)) = 0: c(56) = 0
560 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(16)) = 0: c(16) = 0
160 b(c(17)) = 0: c(17) = 0
170 b(c(27)) = 0: c(27) = 0
270 b(c(38)) = 0: c(38) = 0
380 b(c(39)) = 0: c(39) = 0
390 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 b(c(55)) = 0: c(55) = 0
550 b(c(65)) = 0: c(65) = 0
650 b(c(66)) = 0: c(66) = 0
660 Next j66
b(c(15)) = 0: c(15) = 0
150 b(c(23)) = 0: c(23) = 0
230 b(c(40)) = 0: c(40) = 0
400 b(c(42)) = 0: c(42) = 0
420 b(c(59)) = 0: c(59) = 0
590 b(c(67)) = 0: c(67) = 0
670 Next j67
b(c(13)) = 0: c(13) = 0
130 b(c(69)) = 0: c(69) = 0
690 Next j69
b(c(12)) = 0: c(12) = 0
120 b(c(70)) = 0: c(70) = 0
700 Next j70
b(c(11)) = 0: c(11) = 0
110 b(c(19)) = 0: c(19) = 0
190 b(c(63)) = 0: c(63) = 0
630 b(c(71)) = 0: c(71) = 0
710 Next j71
b(c(10)) = 0: c(10) = 0
100 b(c(18)) = 0: c(18) = 0
180 b(c(37)) = 0: c(37) = 0
370 b(c(45)) = 0: c(45) = 0
450 b(c(64)) = 0: c(64) = 0
640 b(c(72)) = 0: c(72) = 0
720 Next j72
b(c(8)) = 0: c(8) = 0
80 b(c(9)) = 0: c(9) = 0
90 b(c(14)) = 0: c(14) = 0
140 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(7)) = 0: c(7) = 0
70 b(c(75)) = 0: c(75) = 0
750 Next j75
b(c(6)) = 0: c(6) = 0
60 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(4)) = 0: c(4) = 0
40 b(c(78)) = 0: c(78) = 0
780 Next j78
b(c(3)) = 0: c(3) = 0
30 b(c(79)) = 0: c(79) = 0
790 Next j79
b(c(2)) = 0: c(2) = 0
20 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
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine BentDia94")
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 = j100
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
