' Generates Almost Perfect Magic Cubes (Symetrical Horizontal Planes) of order 4 for integers 1 thru 64

' Tested with Office 2007 under Windows 7

```Sub MgcCube4c()

Dim a(64), b(64), c(64)

y = MsgBox("Locked", vbCritical, "Routine MgcCube4c")
End

n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 64: s1 = 130

'   Generate data

t1 = Timer

For j64 = m1 To m2                                                          'a(64)
If b(j64) = 0 Then b(j64) = j64: c(64) = j64 Else GoTo 640
a(64) = j64

a(16) = 65 - a(64): If a(16) <= 0 Or a(16) > 64 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160

For j63 = m1 To m2                                                          'a(63)
If b(j63) = 0 Then b(j63) = j63: c(63) = j63 Else GoTo 630
a(63) = j63

a(15) = 65 - a(63): If a(15) <= 0 Or a(15) > 64 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150

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(61) = 130 - a(62) - a(63) - a(64): If a(61) <= 0 Or a(61) > 64 Then GoTo 610
If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
a(14) = 65 - a(62): If a(14) <= 0 Or a(14) > 64 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = -65 + a(62) + a(63) + a(64): If a(13) <= 0 Or a(13) > 64 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130

For j60 = m1 To m2                                                          'a(60)
If b(j60) = 0 Then b(j60) = j60: c(60) = j60 Else GoTo 600
a(60) = j60

a(55) = -65 + a(60) + a(62) + a(64)
If a(55) <= 0 Or a(55) > 64 Then GoTo 550
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(12) = 65 - a(60): If a(12) <= 0 Or a(12) > 64 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(7) = 130 - a(60) - a(62) - a(64): If a(7) <= 0 Or a(7) > 64 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70

For j59 = m1 To m2                                                           'a(59)
If b(j59) = 0 Then b(j59) = j59: c(59) = j59 Else GoTo 590
a(59) = j59

a(53) = -65 + a(59) + a(63) + a(64): If a(53) <= 0 Or a(53) > 64 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(51) = 195 - a(59) - a(60) - a(62) - a(63) - a(64): If a(51) <= 0 Or a(51) > 64 Then GoTo 510
If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
a(50) = -65 + a(59) + a(60) + a(64): If a(50) <= 0 Or a(50) > 64 Then GoTo 500
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(11) = 65 - a(59): If a(11) <= 0 Or a(11) > 64 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(5) = 130 - a(59) - a(63) - a(64): If a(5) <= 0 Or a(5) > 64 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(3) = -130 + a(59) + a(60) + a(62) + a(63) + a(64): If a(3) <= 0 Or a(3) > 64 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 130 - a(59) - a(60) - a(64): If a(2) <= 0 Or a(2) > 64 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20

For j58 = m1 To m2                                                          'a(58)
If b(j58) = 0 Then b(j58) = j58: c(58) = j58 Else GoTo 580
a(58) = j58

a(57) = 130 - a(58) - a(59) - a(60): If a(57) <= 0 Or a(57) > 64 Then GoTo 570
If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(56) = 65 + a(58) - a(63) - a(64): If a(56) <= 0 Or a(56) > 64 Then GoTo 560
If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(54) = 195 - a(58) - a(59) - a(60) - a(62) - a(64): If a(54) <= 0 Or a(54) > 64 Then GoTo 540
If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(52) = 65 - a(58) - a(60) + a(63): If a(52) <= 0 Or a(52) > 64 Then GoTo 520
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(49) = -65 + a(58) + a(60) + a(62): If a(49) <= 0 Or a(49) > 64 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(43) = 130 - 0.5 * a(58) - 0.5 * a(59) - a(60) - 0.5 * a(62) - 0.5 * a(63)
If a(43) <= 0 Or a(43) > 64 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(42) = 0.5 * a(58) + 0.5 * a(59) + a(60) - 0.5 * a(62) - 0.5 * a(63)
If a(42) <= 0 Or a(42) > 64 Then GoTo 420
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(39) = -65 - 0.5 * a(58) + 0.5 * a(59) + 0.5 * a(62) + 1.5 * a(63) + a(64)
If a(39) <= 0 Or a(39) > 64 Then GoTo 390
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(38) = 65 + 0.5 * a(58) - 0.5 * a(59) + 0.5 * a(62) - 0.5 * a(63) - a(64)
If a(38) <= 0 Or a(38) > 64 Then GoTo 380
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(27) = -65 + 0.5 * a(58) + 0.5 * a(59) + a(60) + 0.5 * a(62) + 0.5 * a(63)
If a(27) <= 0 Or a(27) > 64 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(26) = 65 - 0.5 * a(58) - 0.5 * a(59) - a(60) + 0.5 * a(62) + 0.5 * a(63)
If a(26) <= 0 Or a(26) > 64 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(23) = 130 + 0.5 * a(58) - 0.5 * a(59) - 0.5 * a(62) - 1.5 * a(63) - a(64)
If a(23) <= 0 Or a(23) > 64 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = -0.5 * a(58) + 0.5 * a(59) - 0.5 * a(62) + 0.5 * a(63) + a(64)
If a(22) <= 0 Or a(22) > 64 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(10) = 65 - a(58): If a(10) <= 0 Or a(10) > 64 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = -65 + a(58) + a(59) + a(60): If a(9) <= 0 Or a(9) > 64 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = -a(58) + a(63) + a(64): If a(8) <= 0 Or a(8) > 64 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(6) = -130 + a(58) + a(59) + a(60) + a(62) + a(64): If a(6) <= 0 Or a(6) > 64 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(4) = a(58) + a(60) - a(63): If a(4) <= 0 Or a(4) > 64 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(1) = 130 - a(58) - a(60) - a(62): If a(1) <= 0 Or a(1) > 64 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10

For j48 = m1 To m2                                                          'a(48)
If b(j48) = 0 Then b(j48) = j48: c(48) = j48 Else GoTo 480
a(48) = j48

a(33) = -65 - a(48) + a(59) + a(60) + a(63) + a(64)
If a(33) <= 0 Or a(33) > 64 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(32) = 65 - a(48): If a(32) <= 0 Or a(32) > 64 Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(17) = 130 + a(48) - a(59) - a(60) - a(63) - a(64)
If a(17) <= 0 Or a(17) > 64 Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170

For j47 = m1 To m2                                                          'a(47)
If b(j47) = 0 Then b(j47) = j47: c(47) = j47 Else GoTo 470
a(47) = j47

a(46) = -130 + a(47) + a(62) + a(63) + 2 * a(64)
If a(46) <= 0 Or a(46) > 64 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(45) = 260 - 2 * a(47) - a(48) - a(62) - a(63) - 2 * a(64)
If a(45) <= 0 Or a(45) > 64 Then GoTo 450
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(44) = 130 - a(47) - a(48) - 0.5 * a(58) + 0.5 * a(59) - 0.5 * a(62) + 0.5 * a(63) - a(64)
If a(44) <= 0 Or a(44) > 64 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(41) = -130 + a(47) + a(48) + 0.5 * a(58) - 0.5 * a(59) + 1.5 * a(62) + 0.5 * a(63) + a(64)
If a(41) <= 0 Or a(41) > 64 Then GoTo 410
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(40) = 65 - a(47) - a(48) + 0.5 * a(58) + 0.5 * a(59) + a(60) - 0.5 * a(62) - 0.5 * a(63)
If a(40) <= 0 Or a(40) > 64 Then GoTo 400
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(37) = 65 + a(47) + a(48) - 0.5 * a(58) - 0.5 * a(59) - a(60) - 0.5 * a(62) - 0.5 * a(63)
If a(37) <= 0 Or a(37) > 64 Then GoTo 370
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(36) = -65 + 2 * a(47) + a(48) - a(59) - a(60) + a(62) + a(64)
If a(36) <= 0 Or a(36) > 64 Then GoTo 360
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(35) = 65 - a(47) + a(58) + a(60) - a(63) - a(64)
If a(35) <= 0 Or a(35) > 64 Then GoTo 350
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(34) = 195 - a(47) - a(58) - a(60) - a(62) - a(64)
If a(34) <= 0 Or a(34) > 64 Then GoTo 340
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(31) = 65 - a(47): If a(31) <= 0 Or a(31) > 64 Then GoTo 310
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(30) = 195 - a(47) - a(62) - a(63) - 2 * a(64)
If a(30) <= 0 Or a(30) > 64 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(29) = -195 + 2 * a(47) + a(48) + a(62) + a(63) + 2 * a(64)
If a(29) <= 0 Or a(29) > 64 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(28) = -65 + a(47) + a(48) + 0.5 * a(58) - 0.5 * a(59) + 0.5 * a(62) - 0.5 * a(63) + a(64)
If a(28) <= 0 Or a(28) > 64 Then GoTo 280
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(25) = 195 - a(47) - a(48) - 0.5 * a(58) + 0.5 * a(59) - 1.5 * a(62) - 0.5 * a(63) - a(64)
If a(25) <= 0 Or a(25) > 64 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(24) = a(47) + a(48) - 0.5 * a(58) - 0.5 * a(59) - a(60) + 0.5 * a(62) + 0.5 * a(63)
If a(24) <= 0 Or a(24) > 64 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(21) = -a(47) - a(48) + 0.5 * a(58) + 0.5 * a(59) + a(60) + 0.5 * a(62) + 0.5 * a(63)
If a(21) <= 0 Or a(21) > 64 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = 130 - 2 * a(47) - a(48) + a(59) + a(60) - a(62) - a(64)
If a(20) <= 0 Or a(20) > 64 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = a(47) - a(58) - a(60) + a(63) + a(64)
If a(19) <= 0 Or a(19) > 64 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = -130 + a(47) + a(58) + a(60) + a(62) + a(64)
If a(18) <= 0 Or a(18) > 64 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180

n9 = n9 + 1: GoSub 740 'Print results (selected numbers)
'       n9 = n9 + 1: GoSub 750 'Print results (planes 1, 2, 3, 4)
'       n9 = n9 + 1: GoSub 760 'Print results (3d)

b(c(18)) = 0: c(18) = 0
180 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(24)) = 0: c(24) = 0
240 b(c(25)) = 0: c(25) = 0
250 b(c(28)) = 0: c(28) = 0
280 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(34)) = 0: c(34) = 0
340 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 b(c(40)) = 0: c(40) = 0
400 b(c(41)) = 0: c(41) = 0
410 b(c(44)) = 0: c(44) = 0
440 b(c(45)) = 0: c(45) = 0
450 b(c(46)) = 0: c(46) = 0
460 b(c(47)) = 0: c(47) = 0
470 Next j47

b(c(17)) = 0: c(17) = 0
170 b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 b(c(48)) = 0: c(48) = 0
480 Next j48

b(c(1)) = 0: c(1) = 0
10  b(c(4)) = 0: c(4) = 0
40  b(c(6)) = 0: c(6) = 0
60  b(c(8)) = 0: c(8) = 0
80  b(c(9)) = 0: c(9) = 0
90  b(c(10)) = 0: c(10) = 0
100 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(26)) = 0: c(26) = 0
260 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(42)) = 0: c(42) = 0
420 b(c(43)) = 0: c(43) = 0
430 b(c(49)) = 0: c(49) = 0
490 b(c(52)) = 0: c(52) = 0
520 b(c(54)) = 0: c(54) = 0
540 b(c(56)) = 0: c(56) = 0
560 b(c(57)) = 0: c(57) = 0
570 b(c(58)) = 0: c(58) = 0
580 Next j58

b(c(2)) = 0: c(2) = 0
20  b(c(3)) = 0: c(3) = 0
30  b(c(5)) = 0: c(5) = 0
50  b(c(11)) = 0: c(11) = 0
110 b(c(50)) = 0: c(50) = 0
500 b(c(51)) = 0: c(51) = 0
510 b(c(53)) = 0: c(53) = 0
530 b(c(59)) = 0: c(59) = 0
590 Next j59

b(c(7)) = 0: c(7) = 0
70  b(c(12)) = 0: c(12) = 0
120 b(c(55)) = 0: c(55) = 0
550 b(c(60)) = 0: c(60) = 0
600 Next j60

b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(61)) = 0: c(61) = 0
610 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(15)) = 0: c(15) = 0
150 b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(16)) = 0: c(16) = 0
160 b(c(64)) = 0: c(64) = 0
640 Next j64

t2 = Timer

t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcCube4c")

End

'   Print results (selected numbers)

740 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1

Return

'   Print results (planes 11, 12, 13 and 14)

750 n2 = n2 + 1
If n2 = 7 Then
n2 = 1: k1 = k1 + 20: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If

For i0 = 1 To 4
i3 = (4 - i0) * 16
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1 + (i0 - 1) * 5, k2 + i2).Value = a(i3)
Next i2
Next i1
Cells(k1 + (i0 - 1) * 5, k2 + 1).Value = "Plane 1" + CStr(i0)
Next i0

Return

'   Print results (3d)

760 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 29: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 17
End If

For i0 = 1 To 4
i3 = (4 - i0) * 16
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + 1 + (i1 - 1) * 2 + (i0 - 1) * 7, k2 + 7 + (i2 - 1) * 3 - (i1 - 1) * 2).Value = a(i3)
Next i2
Next i1
Next i0

Return

End Sub
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