' Constructs Associated Magic Cubes (6 x 6 x 6)
' Magic Center Planes, Trenkler Principle
' Tested with Office 2007 under Windows 7
Sub MgcCube6c()
Dim c(216), b(6), b1(27), a(216), d(4), s(12)
y = MsgBox("Blocked", 0, "MgcCube6c")
End
Sheets("Klad1").Select
' Define Simple Magic Cube
b1(19) = 10: b1(20) = 8: b1(21) = 24: b1(22) = 5: b1(23) = 21: b1(24) = 16: b1(25) = 27: b1(26) = 13: b1(27) = 2:
b1(10) = 6: b1(11) = 19: b1(12) = 17: b1(13) = 25: b1(14) = 14: b1(15) = 3: b1(16) = 11: b1(17) = 9: b1(18) = 22:
b1(1) = 26: b1(2) = 15: b1(3) = 1: b1(4) = 12: b1(5) = 7: b1(6) = 23: b1(7) = 4: b1(8) = 20: b1(9) = 18:
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 8: s1 = 21
t1 = Timer
' Center Planes
'Row 1
For j108 = m1 To m2 'c(108)
c(108) = j108 - 1
For j107 = m1 To m2 'c(107)
c(107) = j107 - 1
If c(107) = c(108) Then GoTo 1070
For j106 = m1 To m2 'c(106)
c(106) = j106 - 1
For j105 = m1 To m2 'c(105)
c(105) = j105 - 1
If c(105) = c(106) Then GoTo 1050
For j104 = m1 To m2 'c(104)
c(104) = j104 - 1
c(103) = s1 - c(104) - c(105) - c(106) - c(107) - c(108)
If c(103) < 0 Or c(103) > 7 Then GoTo 1040
If c(103) = c(104) Then GoTo 1040
'Diagonal 1
For j101 = m1 To m2 'c(101)
c(101) = j101 - 1
If c(101) = c(107) Or c(101) = c(108) Then GoTo 1010
For j94 = m1 To m2 'c(94)
c(94) = j94 - 1
For j87 = m1 To m2 'c(87)
c(87) = j87 - 1
If c(87) = c(94) Then GoTo 870
If c(87) = 7 - c(94) Then GoTo 870
For j80 = m1 To m2 'c(80)
c(80) = j80 - 1
If c(80) = 7 - c(101) Or c(80) = 7 - c(107) Or c(80) = 7 - c(108) Then GoTo 800
c(73) = s1 - c(80) - c(87) - c(94) - c(101) - c(108)
If c(73) < 0 Or c(73) > 7 Then GoTo 800
If c(73) = c(80) Then GoTo 800
If c(73) = 7 - c(101) Or c(73) = 7 - c(107) Or c(73) = 7 - c(108) Then GoTo 800
'Column 2
For j95 = m1 To m2 'c(95)
c(95) = j95 - 1
For j89 = m1 To m2 'c(89)
c(89) = j89 - 1
If c(89) = c(95) Then GoTo 890
For j83 = m1 To m2 'c(83)
c(83) = j83 - 1
If c(83) = 7 - c(103) Or c(83) = 7 - c(104) Then GoTo 830
c(77) = s1 - c(83) - c(89) - c(95) - c(101) - c(107)
If c(77) < 0 Or c(77) > 7 Then GoTo 830
If c(77) = c(83) Then GoTo 830
If c(77) = 7 - c(103) Or c(77) = 7 - c(104) Then GoTo 830
'Diagonal 2
For j98 = m1 To m2 'c(98)
c(98) = j98 - 1
If c(98) = c(103) Or c(98) = c(104) Then GoTo 980
If c(98) = 7 - c(77) Or c(98) = 7 - c(83) Then GoTo 980
For j93 = m1 To m2 'c(93)
c(93) = j93 - 1
If c(93) = c(87) Or c(93) = c(94) Then GoTo 930
If c(93) = 7 - c(87) Or c(93) = 7 - c(94) Then GoTo 930
For j88 = m1 To m2 'c(88)
c(88) = j88 - 1
If c(88) = c(87) Or c(88) = c(93) Or c(88) = c(94) Then GoTo 880
If c(88) = 7 - c(87) Or c(88) = 7 - c(93) Or c(88) = 7 - c(94) Then GoTo 880
c(78) = s1 - c(83) - c(88) - c(93) - c(98) - c(103)
If c(78) < 0 Or c(78) > 7 Then GoTo 880
If c(78) = c(77) Or c(78) = c(83) Then GoTo 880
If c(78) = 7 - c(98) Or c(78) = 7 - c(103) Or c(78) = 7 - c(104) Then GoTo 880
'Column 5
For j92 = m1 To m2 'c(92)
c(92) = j92 - 1
If c(92) = 7 - c(89) Or c(92) = 7 - c(95) Then GoTo 920
For j86 = m1 To m2 'c(86)
c(86) = j86 - 1
If c(86) = c(92) Then GoTo 860
If c(86) = 7 - c(89) Or c(86) = 7 - c(95) Then GoTo 860
c(74) = s1 - c(80) - c(86) - c(92) - c(98) - c(104)
If c(74) < 0 Or c(74) > 7 Then GoTo 860
If c(74) = c(73) Or c(74) = c(80) Then GoTo 860
If c(74) = 7 - c(101) Or c(74) = 7 - c(107) Or c(74) = 7 - c(108) Then GoTo 860
'Row 6
For j75 = m1 To m2 'c(75)
c(75) = j75 - 1
If c(75) = 7 - c(105) Or c(75) = 7 - c(106) Then GoTo 750
c(76) = s1 - c(73) - c(74) - c(75) - c(77) - c(78)
If c(76) < 0 Or c(76) > 7 Then GoTo 750
If c(76) = c(75) Then GoTo 750
If c(76) = 7 - c(105) Or c(76) = 7 - c(106) Then GoTo 750
'Column 3
For j100 = m1 To m2 'c(100)
c(100) = j100 - 1
If c(100) = c(105) Or c(100) = c(106) Then GoTo 1000
If c(100) = 7 - c(75) Or c(100) = 7 - c(76) Then GoTo 1000
c(82) = s1 - c(76) - c(88) - c(94) - c(100) - c(106)
If c(82) < 0 Or c(82) > 7 Then GoTo 1000
If c(82) = c(75) Or c(82) = c(76) Then GoTo 1000
If c(82) = 7 - c(100) Or c(82) = 7 - c(105) Or c(82) = 7 - c(106) Then GoTo 1000
'Column 4
For j99 = m1 To m2 'c(99)
c(99) = j99 - 1
If c(99) = c(100) Or c(99) = c(105) Or c(99) = c(106) Then GoTo 990
If c(99) = 7 - c(75) Or c(99) = 7 - c(76) Or c(99) = 7 - c(82) Then GoTo 990
c(81) = s1 - c(75) - c(87) - c(93) - c(99) - c(105)
If c(81) < 0 Or c(81) > 7 Then GoTo 990
If c(81) = c(75) Or c(81) = c(76) Or c(81) = c(82) Then GoTo 990
If c(81) = 7 - c(99) Or c(81) = 7 - c(100) Or c(81) = 7 - c(105) Or c(81) = 7 - c(106) Then GoTo 1000
'Row 3
For j96 = m1 To m2 'c(96)
c(96) = j96 - 1
If c(96) = c(89) Or c(96) = c(95) Then GoTo 960
If c(96) = 7 - c(86) Or c(96) = 7 - c(92) Then GoTo 960
c(91) = s1 - c(92) - c(93) - c(94) - c(95) - c(96)
If c(91) < 0 Or c(91) > 7 Then GoTo 960
If c(91) = c(86) Or c(91) = c(92) Then GoTo 960
If c(91) = 7 - c(89) Or 7 - c(95) = 7 - c(96) Then GoTo 960
'Row 4
For j90 = m1 To m2 'c(90)
c(90) = j90 - 1
If c(90) = c(89) Or c(90) = c(95) Or c(90) = c(96) Then GoTo 900
If c(90) = 7 - c(86) Or c(90) = 7 - c(91) Or c(90) = 7 - c(92) Then GoTo 900
c(85) = s1 - c(86) - c(87) - c(88) - c(89) - c(90)
If c(85) < 0 Or c(85) > 7 Then GoTo 900
If c(85) = c(86) Or c(85) = c(91) Or c(85) = c(92) Then GoTo 900
If c(85) = 7 - c(89) Or c(85) = 7 - c(90) Or c(85) = 7 - c(95) Or c(85) = 7 - c(96) Then GoTo 900
'Remainder
For j84 = m1 To m2 'c(84)
c(84) = j84 - 1
If c(84) = c(77) Or c(84) = c(78) Or c(84) = c(83) Then GoTo 840
If c(84) = 7 - c(98) Or c(84) = 7 - c(103) Or c(84) = 7 - c(104) Then GoTo 840
c(79) = s1 - c(80) - c(81) - c(82) - c(83) - c(84)
If c(79) < 0 Or c(79) > 7 Then GoTo 840
If c(79) = c(73) Or c(79) = c(74) Or c(79) = c(80) Then GoTo 840
If c(79) = 7 - c(101) Or c(79) = 7 - c(107) Or c(79) = 7 - c(108) Then GoTo 840
c(97) = s1 - c(73) - c(79) - c(85) - c(91) - c(103)
If c(97) < 0 Or c(97) > 7 Then GoTo 840
If c(97) = c(103) Or c(97) = c(104) Or c(97) = c(98) Then GoTo 840
If c(97) = 7 - c(77) Or c(97) = 7 - c(78) Or c(97) = 7 - c(83) Or c(97) = 7 - c(84) Then GoTo 840
c(102) = s1 - c(84) - c(90) - c(96) - c(78) - c(108)
If c(102) < 0 Or c(102) > 7 Then GoTo 840
If c(102) = c(101) Or c(102) = c(107) Or c(102) = c(108) Then GoTo 840
If c(102) = 7 - c(97) Or c(102) = 7 - c(98) Or c(102) = 7 - c(103) Or c(102) = 7 - c(104) Then GoTo 840
i2 = 109
For i1 = 109 To 144
i2 = i2 - 1
c(i1) = 7 - c(i2)
Next i1
'Center Plane L3
'Diagonals
For j183 = m1 To m2
c(183) = j183 - 1
For j153 = m1 To m2
c(153) = j153 - 1
If c(153) = c(183) Then GoTo 1530
For j63 = m1 To m2
c(63) = j63 - 1
If c(63) = 7 - c(153) Or c(63) = 7 - c(183) Then GoTo 630
c(33) = s1 - c(63) - c(93) - c(123) - c(153) - c(183)
If c(33) < 0 Or c(33) > 7 Then GoTo 630
If c(33) = c(63) Then GoTo 630
If c(33) = 7 - c(153) Or c(33) = 7 - c(183) Then GoTo 630
For j213 = m1 To m2
c(213) = j213 - 1
For j171 = m1 To m2
c(171) = j171 - 1
If c(171) = c(213) Then GoTo 1710
For j45 = m1 To m2
c(45) = j45 - 1
If c(45) = 7 - c(171) Or c(45) = 7 - c(213) Then GoTo 450
c(3) = s1 - c(45) - c(87) - c(129) - c(171) - c(213)
If c(3) < 0 Or c(3) > 7 Then GoTo 450
If c(3) = c(45) Then GoTo 450
If c(3) = 7 - c(171) Or c(3) = 7 - c(213) Then GoTo 450
For j27 = m1 To m2
c(27) = j27 - 1
If c(27) = c(33) Or c(27) = c(63) Then GoTo 270
If c(27) = 7 - c(153) Or c(27) = 7 - c(183) Then GoTo 270
c(207) = s1 - c(171) - c(135) - c(99) - c(63) - c(27)
If c(207) < 0 Or c(207) > 7 Then GoTo 270
If c(207) = c(171) Or c(207) = c(213) Then GoTo 270
If c(207) = 7 - c(3) Or c(207) = 7 - c(45) Then GoTo 270
For j9 = m1 To m2
c(9) = j9 - 1
If c(9) = c(3) Or c(9) = c(45) Then GoTo 90
If c(9) = 7 - c(171) Or c(9) = 7 - c(207) Or c(9) = 7 - c(213) Then GoTo 90
c(189) = s1 - c(153) - c(117) - c(81) - c(45) - c(9)
If c(189) < 0 Or c(189) > 7 Then GoTo 90
If c(189) = c(153) Or c(189) = c(183) Then GoTo 90
If c(189) = 7 - c(27) Or c(189) = 7 - c(33) Or c(189) = 7 - c(63) Then GoTo 90
For j21 = m1 To m2
c(21) = j21 - 1
c(15) = s1 - c(3) - c(9) - c(21) - c(27) - c(33)
If c(15) < 0 Or c(15) > 7 Then GoTo 90
If c(15) = c(21) Then GoTo 210
For j201 = m1 To m2
c(201) = j201 - 1
If c(201) = 7 - c(15) Or c(201) = 7 - c(21) Then GoTo 2010
c(195) = s1 - c(183) - c(189) - c(201) - c(207) - c(213)
If c(195) < 0 Or c(195) > 7 Then GoTo 2010
If c(195) = c(201) Then GoTo 2010
If c(195) = 7 - c(15) Or c(195) = 7 - c(21) Then GoTo 2010
For j57 = m1 To m2
c(57) = j57 - 1
If c(57) = c(15) Or c(57) = c(21) Then GoTo 570
If c(57) = 7 - c(195) Or c(57) = 7 - c(201) Then GoTo 570
c(165) = s1 - c(201) - c(129) - c(93) - c(57) - c(21)
If c(165) < 0 Or c(165) > 7 Then GoTo 570
If c(165) = c(195) Or c(165) = c(201) Then GoTo 570
If c(165) = 7 - c(15) Or c(165) = 7 - c(21) Or c(165) = 7 - c(57) Then GoTo 570
For j51 = m1 To m2
c(51) = j51 - 1
If c(51) = c(15) Or c(51) = c(21) Or c(51) = c(57) Then GoTo 510
If c(51) = 7 - c(165) Or c(51) = 7 - c(195) Or c(51) = 7 - c(201) Then GoTo 510
c(159) = s1 - c(195) - c(123) - c(87) - c(51) - c(15)
If c(159) < 0 Or c(159) > 7 Then GoTo 510
If c(159) = c(165) Or c(159) = c(195) Or c(159) = c(201) Then GoTo 510
If c(159) = 7 - c(15) Or c(159) = 7 - c(21) Or c(159) = 7 - c(51) Or c(159) = 7 - c(57) Then GoTo 510
For j39 = m1 To m2
c(39) = j39 - 1
If c(39) = c(3) Or c(39) = c(9) Or c(39) = c(45) Then GoTo 390
If c(39) = 7 - c(171) Or c(39) = 7 - c(207) Or c(39) = 7 - c(213) Then GoTo 390
c(69) = s1 - c(39) - c(45) - c(51) - c(57) - c(63)
If c(69) < 0 Or c(69) > 7 Then GoTo 390
If c(69) = c(27) Or c(69) = c(33) Or c(69) = c(63) Then GoTo 390
If c(69) = 7 - c(153) Or c(69) = 7 - c(183) Or c(69) = 7 - c(189) Then GoTo 390
c(177) = s1 - c(213) - c(141) - c(105) - c(69) - c(33)
If c(177) < 0 Or c(177) > 7 Then GoTo 390
If c(177) = c(171) Or c(177) = c(207) Or c(177) = c(213) Then GoTo 390
If c(177) = 7 - c(3) Or c(177) = 7 - c(9) Or c(177) = 7 - c(39) Or c(177) = 7 - c(45) Then GoTo 390
c(147) = s1 - c(153) - c(159) - c(165) - c(171) - c(177)
If c(147) < 0 Or c(147) > 7 Then GoTo 390
If c(147) = c(153) Or c(147) = c(183) Or c(147) = c(189) Then GoTo 390
If c(147) = 7 - c(27) Or c(147) = 7 - c(33) Or c(147) = 7 - c(63) Or c(147) = 7 - c(69) Then GoTo 390
c(184) = 7 - c(33): c(190) = 7 - c(27): c(196) = 7 - c(21): c(202) = 7 - c(15): c(208) = 7 - c(9): c(214) = 7 - c(3):
c(148) = 7 - c(69): c(154) = 7 - c(63): c(160) = 7 - c(57): c(166) = 7 - c(51): c(172) = 7 - c(45): c(178) = 7 - c(39):
c(40) = 7 - c(177): c(46) = 7 - c(171): c(52) = 7 - c(165): c(58) = 7 - c(159): c(64) = 7 - c(153): c(70) = 7 - c(147):
c(4) = 7 - c(213): c(10) = 7 - c(207): c(16) = 7 - c(201): c(22) = 7 - c(195): c(28) = 7 - c(189): c(34) = 7 - c(183):
For j24 = m1 To m2
c(24) = j39 - 1
For j59 = m1 To m2
c(59) = j59 - 1
If c(59) = c(24) Then GoTo 590
For j164 = m1 To m2
c(164) = j164 - 1
If c(164) = 7 - c(59) Or c(164) = 7 - c(24) Then GoTo 1640
c(199) = s1 - c(164) - c(129) - c(94) - c(59) - c(24)
If c(199) < 0 Or c(199) > 7 Then GoTo 1640
If c(199) = c(164) Then GoTo 1640
If c(199) = 7 - c(59) Or c(199) = 7 - c(24) Then GoTo 1640
For j19 = m1 To m2
c(19) = j19 - 1
For j56 = m1 To m2
c(56) = j56 - 1
If c(56) = c(19) Then GoTo 560
c(167) = (2*s1-2*c(56)-2*c(164)-2*c(59)-c(165)-c(166)+c(127)-c(129)-c(130)+c(132)+c(91)-c(93)-c(94)+c(96)-c(57)-c(58))/2
If c(167) < 0 Or c(167) > 7 Or CInt(c(167)) <> c(167) Then GoTo 560
If c(167) = 7 - c(56) Or c(167) = 7 - c(19) Then GoTo 560
c(204) = s1 - c(167) - c(130) - c(93) - c(56) - c(19)
If c(204) < 0 Or c(204) > 7 Then GoTo 560
If c(204) = c(167) Then GoTo 560
If c(204) = 7 - c(56) Or c(204) = 7 - c(19) Then GoTo 560
For j23 = m1 To m2
c(23) = j23 - 1
If c(23) = c(24) Or c(23) = c(59) Then GoTo 230
If c(23) = 7 - c(164) Or c(23) = 7 - c(199) Then GoTo 230
c(20) = s1 - c(23) - c(19) - c(24) - c(21) - c(22)
If c(20) < 0 Or c(20) > 7 Then GoTo 230
If c(20) = c(19) Or c(20) = c(56) Then GoTo 230
If c(20) = 7 - c(167) Or c(20) = 7 - c(204) Then GoTo 230
For j60 = m1 To m2
c(60) = j60 - 1
If c(60) = c(23) Or c(60) = c(24) Or c(60) = c(59) Then GoTo 600
If c(60) = 7 - c(164) Or c(60) = 7 - c(199) Then GoTo 600
c(55) = s1 - c(60) - c(56) - c(59) - c(57) - c(58)
If c(55) < 0 Or c(55) > 7 Then GoTo 600
If c(55) = c(19) Or c(55) = c(20) Or c(55) = c(56) Then GoTo 600
If c(55) = 7 - c(167) Or c(55) = 7 - c(204) Then GoTo 600
c(168) = s1 - c(60) - c(204) - c(24) - c(132) - c(96)
If c(168) < 0 Or c(168) > 7 Then GoTo 600
If c(168) = c(167) Or c(168) = c(204) Then GoTo 600
If c(168) = 7 - c(19) Or c(168) = 7 - c(20) Or c(168) = 7 - c(55) Or c(168) = 7 - c(56) Then GoTo 600
c(163) = s1 - c(55) - c(19) - c(199) - c(127) - c(91)
If c(163) < 0 Or c(163) > 7 Then GoTo 600
If c(163) = c(164) Or c(163) = c(199) Then GoTo 600
If c(163) = 7 - c(23) Or c(163) = 7 - c(24) Or c(163) = 7 - c(59) Or c(163) = 7 - c(60) Then GoTo 600
c(203) = s1 - c(23) - c(167) - c(59) - c(131) - c(95)
If c(203) < 0 Or c(203) > 7 Then GoTo 600
If c(203) = c(167) Or c(203) = c(168) Or c(203) = c(204) Then GoTo 600
If c(203) = 7 - c(19) Or c(203) = 7 - c(20) Or c(203) = 7 - c(55) Or c(203) = 7 - c(56) Then GoTo 600
c(200) = s1 - c(20) - c(56) - c(164) - c(128) - c(92)
If c(200) < 0 Or c(200) > 7 Then GoTo 600
If c(200) = c(163) Or c(200) = c(164) Or c(200) = c(199) Then GoTo 600
If c(200) = 7 - c(23) Or c(200) = 7 - c(24) Or c(200) = 7 - c(59) Or c(200) = 7 - c(60) Then GoTo 600
c(193) = 7 - c(24): c(194) = 7 - c(23): c(197) = 7 - c(20): c(198) = 7 - c(19):
c(157) = 7 - c(60): c(158) = 7 - c(59): c(161) = 7 - c(56): c(162) = 7 - c(55):
c(49) = 7 - c(168): c(50) = 7 - c(167): c(53) = 7 - c(164): c(54) = 7 - c(163):
c(13) = 7 - c(204): c(14) = 7 - c(203): c(17) = 7 - c(200): c(18) = 7 - c(199):
n6 = n6 + 1
Cells(k1, 1).Select: Cells(k1, 1).Value = n6
' Top/Bottom Planes
For j36 = m1 To m2
c(36) = j36 - 1
For j35 = m1 To m2
c(35) = j35 - 1
If c(35) = c(36) Then GoTo 350
For j32 = m1 To m2
c(32) = j32 - 1
c(31) = s1 - c(32) - c(35) - c(36) - c(33) - c(34)
If c(31) < 0 Or c(31) > 7 Then GoTo 320
If c(31) = c(32) Then GoTo 320
For j30 = m1 To m2
c(30) = j30 - 1
If c(30) = c(35) Or c(30) = c(36) Then GoTo 300
For j29 = m1 To m2
c(29) = j29 - 1
If c(29) = c(30) Or c(29) = c(35) Or c(29) = c(36) Then GoTo 290
For j26 = m1 To m2
c(26) = j26 - 1
If c(26) = c(31) Or c(26) = c(32) Then GoTo 260
c(25) = s1 - c(26) - c(29) - c(30) - c(27) - c(28)
If c(25) < 0 Or c(25) > 7 Then GoTo 260
If c(25) = c(26) Or c(25) = c(31) Or c(25) = c(32) Then GoTo 260
For j12 = m1 To m2
c(12) = j12 - 1
c(6) = s1 - c(12) - c(30) - c(36) - c(18) - c(24)
If c(6) < 0 Or c(6) > 7 Then GoTo 120
If c(6) = c(12) Then GoTo 120
For j11 = m1 To m2
c(11) = j11 - 1
If c(11) = c(6) Or c(11) = c(12) Then GoTo 110
c(5) = s1 - c(11) - c(29) - c(35) - c(17) - c(23)
If c(5) < 0 Or c(5) > 7 Then GoTo 110
If c(5) = c(6) Or c(5) = c(11) Or c(5) = c(12) Then GoTo 110
For j8 = m1 To m2
c(8) = j8 - 1
c(7) = s1 - c(8) - c(11) - c(12) - c(9) - c(10)
If c(7) < 0 Or c(7) > 7 Then GoTo 80
If c(7) = c(8) Then GoTo 80
c(2) = s1 - c(8) - c(26) - c(32) - c(14) - c(20)
If c(2) < 0 Or c(2) > 7 Then GoTo 80
If c(2) = c(7) Or c(2) = c(8) Then GoTo 80
c(1) = s1 - c(7) - c(25) - c(31) - c(13) - c(19)
If c(1) < 0 Or c(1) > 7 Then GoTo 80
If c(1) = c(2) Or c(1) = c(7) Or c(1) = c(8) Then GoTo 80
c(181) = 7 - c(36): c(182) = 7 - c(35): c(185) = 7 - c(32): c(186) = 7 - c(31):
c(187) = 7 - c(30): c(188) = 7 - c(29): c(191) = 7 - c(26): c(192) = 7 - c(25):
c(205) = 7 - c(12): c(206) = 7 - c(11): c(209) = 7 - c(8): c(210) = 7 - c(7):
c(211) = 7 - c(6): c(212) = 7 - c(5): c(215) = 7 - c(2): c(216) = 7 - c(1):
For j180 = m1 To m2
c(180) = j180 - 1
If c(180) = c(209) Or c(180) = c(210) Or c(180) = c(215) Or c(180) = c(216) Then GoTo 1800
For j179 = m1 To m2
c(179) = j179 - 1
If c(179) = c(180) Then GoTo 1790
If c(179) = c(209) Or c(179) = c(210) Or c(179) = c(215) Or c(179) = c(216) Then GoTo 1790
For j176 = m1 To m2
c(176) = j176 - 1
If c(176) = c(205) Or c(176) = c(206) Or c(176) = c(211) Or c(176) = c(212) Then GoTo 1760
c(175) = s1 - c(176) - c(177) - c(178) - c(179) - c(180)
If c(175) < 0 Or c(175) > 7 Then GoTo 1760
If c(175) = c(176) Then GoTo 1760
If c(175) = c(205) Or c(175) = c(206) Or c(175) = c(211) Or c(175) = c(212) Then GoTo 1760
For j174 = m1 To m2
c(174) = j174 - 1
If c(174) = c(179) Or c(174) = c(180) Then GoTo 1740
If c(174) = c(209) Or c(174) = c(210) Or c(174) = c(215) Or c(174) = c(216) Then GoTo 1740
c(173) = 14 - c(174) - c(179) - c(180)
If c(173) < 0 Or c(173) > 7 Then GoTo 1740
If c(173) = c(174) Or c(173) = c(179) Or c(173) = c(180) Then GoTo 1740
If c(173) = c(209) Or c(173) = c(210) Or c(173) = c(215) Or c(173) = c(216) Then GoTo 1740
c(37) = 7 - c(180): c(38) = 7 - c(179)
c(43) = 7 - c(174): c(44) = 7 - c(173)
c(145) = s1 - c(181) - c(109) - c(73) - c(37) - c(1)
If c(145) < 0 Or c(145) > 7 Then GoTo 1740
If c(145) = c(181) Or c(145) = c(182) Or c(145) = c(187) Or c(145) = c(188) Then GoTo 1740
c(146) = s1 - c(182) - c(110) - c(74) - c(38) - c(2)
If c(146) < 0 Or c(146) > 7 Then GoTo 1740
If c(146) = c(145) Then GoTo 1740
If c(146) = c(181) Or c(146) = c(182) Or c(146) = c(187) Or c(146) = c(188) Then GoTo 1740
c(151) = s1 - c(187) - c(115) - c(79) - c(43) - c(7)
If c(151) < 0 Or c(151) > 7 Then GoTo 1740
If c(151) = c(145) Or c(151) = c(146) Then GoTo 1740
If c(151) = c(181) Or c(151) = c(182) Or c(151) = c(187) Or c(151) = c(188) Then GoTo 1740
c(152) = s1 - c(188) - c(116) - c(80) - c(44) - c(8)
If c(152) < 0 Or c(152) > 7 Then GoTo 1740
If c(152) = c(145) Or c(152) = c(146) Or c(152) = c(151) Then GoTo 1740
If c(152) = c(181) Or c(152) = c(182) Or c(152) = c(187) Or c(152) = c(188) Then GoTo 1740
c(65) = 7 - c(152): c(66) = 7 - c(151)
c(71) = 7 - c(146): c(72) = 7 - c(145)
c(170) = s1 - c(146) - c(152) - c(158) - c(164) - c(176)
If c(170) < 0 Or c(170) > 7 Then GoTo 1740
If c(170) = c(205) Or c(170) = c(206) Or c(170) = c(211) Or c(170) = c(212) Then GoTo 1740
c(169) = s1 - c(145) - c(151) - c(157) - c(163) - c(175)
If c(169) < 0 Or c(169) > 7 Then GoTo 1740
If c(169) = c(205) Or c(169) = c(206) Or c(169) = c(211) Or c(169) = c(212) Then GoTo 1740
c(61) = s1 - c(205) - c(169) - c(133) - c(97) - c(25)
If c(61) < 0 Or c(61) > 7 Then GoTo 1740
If c(61) = c(25) Or c(61) = c(26) Or c(61) = c(31) Or c(61) = c(32) Then GoTo 1740
c(62) = s1 - c(206) - c(170) - c(134) - c(98) - c(26)
If c(62) < 0 Or c(62) > 7 Then GoTo 1740
If c(62) = c(61) Then GoTo 1740
If c(62) = c(25) Or c(62) = c(26) Or c(62) = c(31) Or c(62) = c(32) Then GoTo 1740
c(67) = s1 - c(211) - c(175) - c(139) - c(103) - c(31)
If c(67) < 0 Or c(67) > 7 Then GoTo 1740
If c(67) = c(61) Or c(67) = c(62) Then GoTo 1740
If c(67) = c(25) Or c(67) = c(26) Or c(67) = c(31) Or c(67) = c(32) Then GoTo 1740
c(68) = s1 - c(212) - c(176) - c(140) - c(104) - c(32)
If c(68) < 0 Or c(68) > 7 Then GoTo 1740
If c(68) = c(61) Or c(68) = c(62) Or c(68) = c(67) Then GoTo 1740
If c(68) = c(25) Or c(68) = c(26) Or c(68) = c(31) Or c(68) = c(32) Then GoTo 1740
c(149) = 7 - c(68): c(150) = 7 - c(67)
c(155) = 7 - c(62): c(156) = 7 - c(61)
c(41) = s1 - c(185) - c(149) - c(113) - c(77) - c(5)
If c(41) < 0 Or c(41) > 7 Then GoTo 1740
If c(41) = c(5) Or c(41) = c(6) Or c(41) = c(11) Or c(41) = c(12) Then GoTo 1740
c(42) = s1 - c(186) - c(150) - c(114) - c(78) - c(6)
If c(42) < 0 Or c(42) > 7 Then GoTo 1740
If c(42) = c(11) Then GoTo 1740
If c(42) = c(5) Or c(42) = c(6) Or c(42) = c(11) Or c(42) = c(12) Then GoTo 1740
c(47) = s1 - c(191) - c(155) - c(119) - c(83) - c(11)
If c(47) < 0 Or c(47) > 7 Then GoTo 1740
If c(47) = c(41) Or c(47) = c(42) Then GoTo 1740
If c(47) = c(5) Or c(47) = c(6) Or c(47) = c(11) Or c(47) = c(12) Then GoTo 1740
c(48) = s1 - c(192) - c(156) - c(120) - c(84) - c(12)
If c(48) < 0 Or c(48) > 7 Then GoTo 1740
If c(48) = c(41) Or c(48) = c(42) Or c(48) = c(47) Then GoTo 1740
If c(48) = c(5) Or c(48) = c(6) Or c(48) = c(11) Or c(48) = c(12) Then GoTo 1740
MC6 = 21: GoSub 2000: If fl1 = 0 Then GoTo 5 'Back Check Trenkler Cube
GoSub 2800 'Contruct Simple Magic Cube
GoSub 2850: If fl1 = 0 Then GoTo 1740 'Back Check Identical Numbers
n9 = n9 + 1: GoSub 2750 'Print Cube
5
1740 Next j174
1760 Next j176
1790 Next j179
1800 Next j180
80 Next j8
110 Next j11
120 Next j12
260 Next j26
290 Next j29
300 Next j30
320 Next j32
350 Next j35
360 Next j36
600 Next j60
230 Next j23
560 Next j56
190 Next j19
1640 Next j164
590 Next j59
240 Next j24
390 Next j39
510 Next j51
570 Next j57
2010 Next j201
210 Next j21
90 Next j9
270 Next j27
450 Next j45
1710 Next j171
2130 Next j213
630 Next j63
1530 Next j153
1830 Next j183
840 Next j84
900 Next j90
960 Next j96
990 Next j99
1000 Next j100
750 Next j75
860 Next j86
920 Next j92
880 Next j88
930 Next j93
980 Next j98
830 Next j83
890 Next j89
950 Next j95
800 Next j80
870 Next j87
940 Next j94
1010 Next j101
1040 Next j104
1050 Next j105
1060 Next j106
1070 Next j107
1080 Next j108
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine MgcCube6c")
End
' Back Check Magic Constant
2000 fl1 = 1
' Rows
i1 = -5
For i0 = 1 To 36
i1 = i1 + 6
b(1) = c(i1): b(2) = c(i1 + 1): b(3) = c(i1 + 2): b(4) = c(i1 + 3): b(5) = c(i1 + 4): b(6) = c(i1 + 5)
GoSub 2860
If fl1 = 0 Then Return
Next i0
' Columns
i1 = 0: i2 = 0
For i0 = 1 To 36
i1 = i1 + 1
b(1) = c(i1): b(2) = c(i1 + 6): b(3) = c(i1 + 12): b(4) = c(i1 + 18): b(5) = c(i1 + 24): b(6) = c(i1 + 30)
i2 = i2 + 1: If i2 = 6 Then i2 = 0: i1 = i1 + 30
GoSub 2860
If fl1 = 0 Then Return
Next i0
' Pillars
i1 = 0: i2 = 0
For i0 = 1 To 36
i1 = i0
b(1) = c(i1): b(2) = c(i1 + 36): b(3) = c(i1 + 72): b(4) = c(i1 + 108): b(5) = c(i1 + 144): b(6) = c(i1 + 180)
GoSub 2860
If fl1 = 0 Then Return
Next i0
' Accociated Pairs
For i1 = 1 To 108
s2 = c(i1) + c(216 + 1 - i1)
If s2 <> 7 Then fl1 = 0: Return
Next i1
' Plane Diagonals
' Hor Planes
s(1) = c(109) + c(116) + c(123) + c(130) + c(137) + c(144)
s(2) = c(139) + c(134) + c(129) + c(124) + c(119) + c(114)
s(3) = c(73) + c(80) + c(87) + c(94) + c(101) + c(108)
s(4) = c(103) + c(98) + c(93) + c(88) + c(83) + c(78)
' Vert Planes L/R
s(5) = c(183) + c(153) + c(123) + c(93) + c(63) + c(33)
s(6) = c(184) + c(154) + c(124) + c(94) + c(64) + c(34)
s(7) = c(213) + c(171) + c(129) + c(87) + c(45) + c(3)
s(8) = c(214) + c(172) + c(130) + c(88) + c(46) + c(4)
' Vert Planes B/F
s(9) = c(193) + c(158) + c(123) + c(88) + c(53) + c(18)
s(10) = c(198) + c(161) + c(124) + c(87) + c(50) + c(13)
s(11) = c(199) + c(164) + c(129) + c(94) + c(59) + c(24)
s(12) = c(204) + c(167) + c(130) + c(93) + c(56) + c(19)
fl1 = 1
For i1 = 1 To 12
If s(i1) <> MC6 Then fl1 = 0: Return
Next i1
Return
' Check MC6
2860 fl1 = 1
If b(1) + b(2) + b(3) + b(4) + b(5) + b(6) <> MC6 Then fl1 = 0
Return
' Print Cubes (6 plane format)
2750 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 42: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
For i0 = 1 To 6
i3 = (6 - i0) * 36
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1 + (i0 - 1) * 7, k2 + i2).Value = c(i3) 'Trenkler Cube
' Cells(k1 + i1 + (i0 - 1) * 7, k2 + i2).Value = a(i3) 'Simple Magic Cube
Next i2
Next i1
Next i0
Return
' Calculate Simple Magic Cubes
2800
a(181) = b1(19) + 27 * c(181): a(182) = b1(19) + 27 * c(182): a(183) = b1(20) + 27 * c(183):
a(187) = b1(19) + 27 * c(187): a(188) = b1(19) + 27 * c(188): a(189) = b1(20) + 27 * c(189):
a(193) = b1(22) + 27 * c(193): a(194) = b1(22) + 27 * c(194): a(195) = b1(23) + 27 * c(195):
a(199) = b1(22) + 27 * c(199): a(200) = b1(22) + 27 * c(200): a(201) = b1(23) + 27 * c(201):
a(205) = b1(25) + 27 * c(205): a(206) = b1(25) + 27 * c(206): a(207) = b1(26) + 27 * c(207):
a(211) = b1(25) + 27 * c(211): a(212) = b1(25) + 27 * c(212): a(213) = b1(26) + 27 * c(213):
a(184) = b1(20) + 27 * c(184): a(185) = b1(21) + 27 * c(185): a(186) = b1(21) + 27 * c(186):
a(190) = b1(20) + 27 * c(190): a(191) = b1(21) + 27 * c(191): a(192) = b1(21) + 27 * c(192):
a(196) = b1(23) + 27 * c(196): a(197) = b1(24) + 27 * c(197): a(198) = b1(24) + 27 * c(198):
a(202) = b1(23) + 27 * c(202): a(203) = b1(24) + 27 * c(203): a(204) = b1(24) + 27 * c(204):
a(208) = b1(26) + 27 * c(208): a(209) = b1(27) + 27 * c(209): a(210) = b1(27) + 27 * c(210):
a(214) = b1(26) + 27 * c(214): a(215) = b1(27) + 27 * c(215): a(216) = b1(27) + 27 * c(216):
a(145) = b1(19) + 27 * c(145): a(146) = b1(19) + 27 * c(146): a(147) = b1(20) + 27 * c(147):
a(151) = b1(19) + 27 * c(151): a(152) = b1(19) + 27 * c(152): a(153) = b1(20) + 27 * c(153):
a(157) = b1(22) + 27 * c(157): a(158) = b1(22) + 27 * c(158): a(159) = b1(23) + 27 * c(159):
a(163) = b1(22) + 27 * c(163): a(164) = b1(22) + 27 * c(164): a(165) = b1(23) + 27 * c(165):
a(169) = b1(25) + 27 * c(169): a(170) = b1(25) + 27 * c(170): a(171) = b1(26) + 27 * c(171):
a(175) = b1(25) + 27 * c(175): a(176) = b1(25) + 27 * c(176): a(177) = b1(26) + 27 * c(177):
a(148) = b1(20) + 27 * c(148): a(149) = b1(21) + 27 * c(149): a(150) = b1(21) + 27 * c(150):
a(154) = b1(20) + 27 * c(154): a(155) = b1(21) + 27 * c(155): a(156) = b1(21) + 27 * c(156):
a(160) = b1(23) + 27 * c(160): a(161) = b1(24) + 27 * c(161): a(162) = b1(24) + 27 * c(162):
a(166) = b1(23) + 27 * c(166): a(167) = b1(24) + 27 * c(167): a(168) = b1(24) + 27 * c(168):
a(172) = b1(26) + 27 * c(172): a(173) = b1(27) + 27 * c(173): a(174) = b1(27) + 27 * c(174):
a(178) = b1(26) + 27 * c(178): a(179) = b1(27) + 27 * c(179): a(180) = b1(27) + 27 * c(180):
a(109) = b1(10) + 27 * c(109): a(110) = b1(10) + 27 * c(110): a(111) = b1(11) + 27 * c(111):
a(115) = b1(10) + 27 * c(115): a(116) = b1(10) + 27 * c(116): a(117) = b1(11) + 27 * c(117):
a(121) = b1(13) + 27 * c(121): a(122) = b1(13) + 27 * c(122): a(123) = b1(14) + 27 * c(123):
a(127) = b1(13) + 27 * c(127): a(128) = b1(13) + 27 * c(128): a(129) = b1(14) + 27 * c(129):
a(133) = b1(16) + 27 * c(133): a(134) = b1(16) + 27 * c(134): a(135) = b1(17) + 27 * c(135):
a(139) = b1(16) + 27 * c(139): a(140) = b1(16) + 27 * c(140): a(141) = b1(17) + 27 * c(141):
a(112) = b1(11) + 27 * c(112): a(113) = b1(12) + 27 * c(113): a(114) = b1(12) + 27 * c(114):
a(118) = b1(11) + 27 * c(118): a(119) = b1(12) + 27 * c(119): a(120) = b1(12) + 27 * c(120):
a(124) = b1(14) + 27 * c(124): a(125) = b1(15) + 27 * c(125): a(126) = b1(15) + 27 * c(126):
a(130) = b1(14) + 27 * c(130): a(131) = b1(15) + 27 * c(131): a(132) = b1(15) + 27 * c(132):
a(136) = b1(17) + 27 * c(136): a(137) = b1(18) + 27 * c(137): a(138) = b1(18) + 27 * c(138):
a(142) = b1(17) + 27 * c(142): a(143) = b1(18) + 27 * c(143): a(144) = b1(18) + 27 * c(144):
a(73) = b1(10) + 27 * c(73): a(74) = b1(10) + 27 * c(74): a(75) = b1(11) + 27 * c(75):
a(79) = b1(10) + 27 * c(79): a(80) = b1(10) + 27 * c(80): a(81) = b1(11) + 27 * c(81):
a(85) = b1(13) + 27 * c(85): a(86) = b1(13) + 27 * c(86): a(87) = b1(14) + 27 * c(87):
a(91) = b1(13) + 27 * c(91): a(92) = b1(13) + 27 * c(92): a(93) = b1(14) + 27 * c(93):
a(97) = b1(16) + 27 * c(97): a(98) = b1(16) + 27 * c(98): a(99) = b1(17) + 27 * c(99):
a(103) = b1(16) + 27 * c(103): a(104) = b1(16) + 27 * c(104): a(105) = b1(17) + 27 * c(105):
a(76) = b1(11) + 27 * c(76): a(77) = b1(12) + 27 * c(77): a(78) = b1(12) + 27 * c(78):
a(82) = b1(11) + 27 * c(82): a(83) = b1(12) + 27 * c(83): a(84) = b1(12) + 27 * c(84):
a(88) = b1(14) + 27 * c(88): a(89) = b1(15) + 27 * c(89): a(90) = b1(15) + 27 * c(90):
a(94) = b1(14) + 27 * c(94): a(95) = b1(15) + 27 * c(95): a(96) = b1(15) + 27 * c(96):
a(100) = b1(17) + 27 * c(100): a(101) = b1(18) + 27 * c(101): a(102) = b1(18) + 27 * c(102):
a(106) = b1(17) + 27 * c(106): a(107) = b1(18) + 27 * c(107): a(108) = b1(18) + 27 * c(108):
a(37) = b1(1) + 27 * c(37): a(38) = b1(1) + 27 * c(38): a(39) = b1(2) + 27 * c(39):
a(43) = b1(1) + 27 * c(43): a(44) = b1(1) + 27 * c(44): a(45) = b1(2) + 27 * c(45):
a(49) = b1(4) + 27 * c(49): a(50) = b1(4) + 27 * c(50): a(51) = b1(5) + 27 * c(51):
a(55) = b1(4) + 27 * c(55): a(56) = b1(4) + 27 * c(56): a(57) = b1(5) + 27 * c(57):
a(61) = b1(7) + 27 * c(61): a(62) = b1(7) + 27 * c(62): a(63) = b1(8) + 27 * c(63):
a(67) = b1(7) + 27 * c(67): a(68) = b1(7) + 27 * c(68): a(69) = b1(8) + 27 * c(69):
a(40) = b1(2) + 27 * c(40): a(41) = b1(3) + 27 * c(41): a(42) = b1(3) + 27 * c(42):
a(46) = b1(2) + 27 * c(46): a(47) = b1(3) + 27 * c(47): a(48) = b1(3) + 27 * c(48):
a(52) = b1(5) + 27 * c(52): a(53) = b1(6) + 27 * c(53): a(54) = b1(6) + 27 * c(54):
a(58) = b1(5) + 27 * c(58): a(59) = b1(6) + 27 * c(59): a(60) = b1(6) + 27 * c(60):
a(64) = b1(8) + 27 * c(64): a(65) = b1(9) + 27 * c(65): a(66) = b1(9) + 27 * c(66):
a(70) = b1(8) + 27 * c(70): a(71) = b1(9) + 27 * c(71): a(72) = b1(9) + 27 * c(72):
a(1) = b1(1) + 27 * c(1): a(2) = b1(1) + 27 * c(2): a(3) = b1(2) + 27 * c(3):
a(7) = b1(1) + 27 * c(7): a(8) = b1(1) + 27 * c(8): a(9) = b1(2) + 27 * c(9):
a(13) = b1(4) + 27 * c(13): a(14) = b1(4) + 27 * c(14): a(15) = b1(5) + 27 * c(15):
a(19) = b1(4) + 27 * c(19): a(20) = b1(4) + 27 * c(20): a(21) = b1(5) + 27 * c(21):
a(25) = b1(7) + 27 * c(25): a(26) = b1(7) + 27 * c(26): a(27) = b1(8) + 27 * c(27):
a(31) = b1(7) + 27 * c(31): a(32) = b1(7) + 27 * c(32): a(33) = b1(8) + 27 * c(33):
a(4) = b1(2) + 27 * c(4): a(5) = b1(3) + 27 * c(5): a(6) = b1(3) + 27 * c(6):
a(10) = b1(2) + 27 * c(10): a(11) = b1(3) + 27 * c(11): a(12) = b1(3) + 27 * c(12):
a(16) = b1(5) + 27 * c(16): a(17) = b1(6) + 27 * c(17): a(18) = b1(6) + 27 * c(18):
a(22) = b1(5) + 27 * c(22): a(23) = b1(6) + 27 * c(23): a(24) = b1(6) + 27 * c(24):
a(28) = b1(8) + 27 * c(28): a(29) = b1(9) + 27 * c(29): a(30) = b1(9) + 27 * c(30):
a(34) = b1(8) + 27 * c(34): a(35) = b1(9) + 27 * c(35): a(36) = b1(9) + 27 * c(36):
Return
' Check Identical Numbers (Back Check)
2850 fl1 = 1
For i1 = 1 To 216
a20 = a(i1)
For i2 = i1 + 1 To 216
If a20 = a(i2) Then fl1 = 0: Return
Next i2
Next i1
Return
End Sub
