' Generates Perfect Concentric Magic Cubes of order 6 (Prime Numbers)
' Part II: Anti Symmetric Magic Back Squares (c)
' Tested with Office 365 under Windows 10
' Generates Perfect Concentric Magic Cubes of order 6 (Prime Numbers)
' Part II: Anti Symmetric Magic Back Squares (c)
' Tested with Office 365 under Windows 10
Sub PrimeCubes78c()
Dim a1(724), a(100), b1(43291), b(43291), c(100), a6(72), C6(216)
y = MsgBox("Locked", vbCritical, "Routine PrimeCubes78c")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs63"
ShtNm2 = "TopSqrs6"
Sheets("Klad1").Select
t1 = Timer
For j100 = 275 To 319 '251 restart
' Start Reading Data from ShtNm2
MC6 = Sheets(ShtNm2).Cells(j100, 73).Value
Rcrd1a = Sheets(ShtNm2).Cells(j100, 74).Value
' Read Available Prime Numbers From Sheet ShtNm1
' Read Top and Bottom Plane From Sheet ShtNm2
GoSub 2015
' Define Back Square
Erase a 'Clear Scratch Areas
For i1 = 1 To 6
a(i1) = C6(i1): a(i1 + 30) = C6(i1 + 180)
Next i1
t11 = Timer 'Time Out
For j29 = m2 / 2 To m1 Step -1 'a(29)
If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
a(29) = a1(j29)
a(65) = Pr6 - a(29): If b(a(65)) = 0 Then b(a(65)) = a(65): c(65) = a(65) Else GoTo 650
For j22 = m1 To m2 'a(22)
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
a(22) = a1(j22)
a(58) = Pr6 - a(22): If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
For j15 = m1 To m2 'a(15)
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(51) = Pr6 - a(15): If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
a(8) = s6 - a(15) - a(22) - a(29) - a(1) - a(36)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(44) = Pr6 - a(8): If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
For j23 = m2 / 2 To m2 'a(23)
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
a(59) = Pr6 - a(23): If b(a(59)) = 0 Then b(a(59)) = a(59): c(59) = a(59) Else GoTo 590
For j17 = m1 To m2 'a(17)
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)
a(53) = Pr6 - a(17): If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(11) = s6 - a(17) - a(23) - a(29) - a(5) - a(35)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 110
If b1(a(11)) = 0 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(47) = Pr6 - a(11): If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
For j26 = m1 To m2 'a(26)
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
a(62) = Pr6 - a(26): If b(a(62)) = 0 Then b(a(62)) = a(62): c(62) = a(62) Else GoTo 620
For j21 = m1 To m2 'a(21)
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)
a(57) = Pr6 - a(21): If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(16) = s6 - a(21) - a(26) - a(11) - a(6) - a(31)
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160
If b1(a(16)) = 0 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(52) = Pr6 - a(16): If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
For j20 = m1 To m2 'a(20)
If b(a1(j20)) = 0 Then b(a1(j20)) = a1(j20): c(20) = a1(j20) Else GoTo 200
a(20) = a1(j20)
a(56) = Pr6 - a(20): If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(14) = s6 - a(20) - a(26) - a(8) - a(2) - a(32)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(50) = Pr6 - a(14): If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
For j28 = m1 To m2 'a(28)
If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
a(28) = a1(j28)
a(64) = Pr6 - a(28): If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640
a(10) = s6 - a(28) - a(16) - a(22) - a(4) - a(34)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(46) = Pr6 - a(10): If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
For j27 = m1 To m2 'a(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a(27) = a1(j27)
a(63) = Pr6 - a(27): If b(a(63)) = 0 Then b(a(63)) = a(63): c(63) = a(63) Else GoTo 630
a(9) = s6 - a(27) - a(21) - a(15) - a(3) - a(33)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(45) = Pr6 - a(9): If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
For j30 = m1 To m2 'a(30)
If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
a(30) = a1(j30)
a(66) = Pr6 - a(30): If b(a(66)) = 0 Then b(a(66)) = a(66): c(66) = a(66) Else GoTo 660
a(25) = s6 - a(30) - a(27) - a(28) - a(26) - a(29)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(61) = Pr6 - a(25): If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
For j24 = m1 To m2 'a(24)
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(60) = Pr6 - a(24): If b(a(60)) = 0 Then b(a(60)) = a(60): c(60) = a(60) Else GoTo 600
a(19) = s6 - a(24) - a(20) - a(21) - a(23) - a(22)
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(55) = Pr6 - a(19): If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
For j18 = m1 To m2 'a(18)
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 180
a(18) = a1(j18)
a(54) = Pr6 - a(18): If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(13) = s6 - a(18) - a(14) - a(16) - a(17) - a(15)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130
If b1(a(13)) = 0 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(49) = Pr6 - a(13): If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(12) = s6 - a(30) - a(18) - a(24) - a(6) - a(36)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(48) = Pr6 - a(12): If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(7) = s6 - a(12) - a(9) - a(10) - a(11) - a(8)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(43) = Pr6 - a(7): If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
GoSub 850 'Exclude solutions with identical numbers (back check)
If fl1 = 0 Then GoTo 5
GoSub 800 'Fill Cube Back and Front Square_
'' n9 = n9 + 1: GoSub 1740 'Print results (selected numbers Back and Front Square_
n9 = n9 + 1: GoSub 1750 'Print results (Back Square)
Erase b, c: GoTo 1000 'Print only first Back Square
5
b(c(43)) = 0: c(43) = 0
430 b(c(7)) = 0: c(7) = 0
70 b(c(48)) = 0: c(48) = 0
480 b(c(12)) = 0: c(12) = 0
120 b(c(49)) = 0: c(49) = 0
490 b(c(13)) = 0: c(13) = 0
130 b(c(54)) = 0: c(54) = 0
540 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(55)) = 0: c(55) = 0
550 b(c(19)) = 0: c(19) = 0
190 b(c(60)) = 0: c(60) = 0
600 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(61)) = 0: c(61) = 0
610 b(c(25)) = 0: c(25) = 0
250 b(c(66)) = 0: c(66) = 0
660 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(45)) = 0: c(45) = 0
450 b(c(9)) = 0: c(9) = 0
90 b(c(63)) = 0: c(63) = 0
630 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(46)) = 0: c(46) = 0
460 b(c(10)) = 0: c(10) = 0
100 b(c(64)) = 0: c(64) = 0
640 b(c(28)) = 0: c(28) = 0
280 Next j28
b(c(50)) = 0: c(50) = 0
500 b(c(14)) = 0: c(14) = 0
140 b(c(56)) = 0: c(56) = 0
560 b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(52)) = 0: c(52) = 0
520 b(c(16)) = 0: c(16) = 0
160 b(c(57)) = 0: c(57) = 0
570 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(62)) = 0: c(62) = 0
620 b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(47)) = 0: c(47) = 0
470 b(c(11)) = 0: c(11) = 0
110 b(c(53)) = 0: c(53) = 0
530 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(59)) = 0: c(59) = 0
590 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(44)) = 0: c(44) = 0
440 b(c(8)) = 0: c(8) = 0
80 b(c(51)) = 0: c(51) = 0
510 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(58)) = 0: c(58) = 0
580 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(65)) = 0: c(65) = 0
650 b(c(29)) = 0: c(29) = 0
290 Next j29
1000 Erase b1, b, c
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s6)
y = MsgBox(t10, 0, "Routine PrimeCubes78c")
End
' Exclude solutions with identical numbers a()
850 fl1 = 1
For j1 = 1 To 36
a20 = a(j1): If a20 = 0 Then GoTo 855
For j2 = (1 + j1) To 36
If a20 = a(j2) Then fl1 = 0: Return
Next j2
855 Next j1
Return
' Print results (selected numbers)
' Not Common with Top / Bottom Square
1740
i3 = 0
For i1 = 7 To 30
i3 = i3 + 1
Cells(n9, i3).Value = a(i1)
Next i1
i3 = 24
For i1 = 67 To 175 Step 36
For i2 = i1 To i1 + 5
i3 = i3 + 1
Cells(n9, i3).Value = C6(i2)
Next i2
Next i1
Cells(n9, 49).Value = s6
Cells(n9, 50).Value = Rcrd1a 'Record Center Cube
Cells(n9, 51).Value = j100 'Record Top Square
Return
' Print results, back square a()
1750 n2 = n2 + 1
If n2 = 4 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(1, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = s6
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
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 = s6 ''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 = C6(i3) 'Bordered Magic Cube
Next i2
Next i1
Next i0
Return
' Fill Cube c6(), Top / Bottom Square
750
' Top Square
For i1 = 1 To 36
C6(i1) = a6(i1)
Next i1
' Bottom Square
For i1 = 37 To 72
C6(i1 - 36 + 180) = a6(i1)
Next i1
Return
' Fill Cube c6(), Back / front Square
800
' Back Square
C6(37) = a(7): C6(38) = a(8): C6(39) = a(9): C6(40) = a(10): C6(41) = a(11): C6(42) = a(12):
C6(73) = a(13): C6(74) = a(14): C6(75) = a(15): C6(76) = a(16): C6(77) = a(17): C6(78) = a(18):
C6(109) = a(19): C6(110) = a(20): C6(111) = a(21): C6(112) = a(22): C6(113) = a(23): C6(114) = a(24):
C6(145) = a(25): C6(146) = a(26): C6(147) = a(27): C6(148) = a(28): C6(149) = a(29): C6(150) = a(30):
' Front Square
C6(67) = Pr6 - C6(42): C6(68) = Pr6 - C6(38): C6(69) = Pr6 - C6(39): C6(70) = Pr6 - C6(40):
C6(71) = Pr6 - C6(41): C6(72) = Pr6 - C6(37):
C6(103) = Pr6 - C6(78): C6(104) = Pr6 - C6(74): C6(105) = Pr6 - C6(75): C6(106) = Pr6 - C6(76):
C6(107) = Pr6 - C6(77): C6(108) = Pr6 - C6(73):
C6(139) = Pr6 - C6(114): C6(140) = Pr6 - C6(110): C6(141) = Pr6 - C6(111): C6(142) = Pr6 - C6(112):
C6(143) = Pr6 - C6(113): C6(144) = Pr6 - C6(109):
C6(175) = Pr6 - C6(150): C6(176) = Pr6 - C6(146): C6(177) = Pr6 - C6(147): C6(178) = Pr6 - C6(148):
C6(179) = Pr6 - C6(149): C6(180) = Pr6 - C6(145):
''n9 = n9 + 1: GoSub 1750: End
Return
' Remove used primes from available primes
950 For i1 = 1 To 72
b1(a6(i1)) = 0
Next i1
Return
' Read Prime Numbers From sheet ShtNm1
2015 Pr6 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value ' Pairsum
nvar1 = Sheets(ShtNm1).Cells(Rcrd1a, 5).Value
s4 = 2 * Pr6 ' MC4
s6 = 3 * Pr6 ' Mc6
Erase b1
For j1 = 1 To nvar1
x = Sheets(ShtNm1).Cells(Rcrd1a, 10 + j1).Value
b1(x) = x
Next j1
pMax = Sheets(ShtNm1).Cells(Rcrd1a, 10 + nvar1).Value
' Read Top Square 6 x 6
For i1 = 1 To 36
a6(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
' Read Bottom Square Square 6 x 6
For i1 = 37 To 72
a6(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
GoSub 750 'Fill Top and Bottom c6()
GoSub 950 'Remove used primes from available primes
' Restore available pairs in a1()
n10 = 0
For j1 = 1 To pMax
If b1(j1) <> 0 Then
n10 = n10 + 1
a1(n10) = b1(j1)
End If
Next j1
m1 = 1: m2 = n10: n10 = 0
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
Return
End Sub
