' Generates Bordered Magic Cubes of order 6 (Prime Numbers)
' Semi Magic Top and Bottom Squares
' Part I: Semi Magic Anti Symmetric Squares (3 x 3)
' Tested with Office 2007 under Windows 7
Sub PrimeCubes6a()
Dim a1(1200), b1(21803), a(9), b(21803), c(9), c6(216)
Dim a2(9), b2(21803), c2(9)
y = MsgBox("Locked", vbCritical, "Routine Priem6a")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs63"
Sheets("Klad1").Select
t1 = Timer
For j100 = 32 To 98
GoSub 3100 'Read Prime Numbers From Sheet ShtNm1
' Generate Semi Magic Squares
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 2090
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 2090
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 2080
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 2080
a(8) = a1(j8)
a(7) = s1 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 2070:
If b1(a(7)) = 0 Then GoTo 2070
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 2070
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 2060
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 2060
a(6) = a1(j6)
a(3) = s1 - a(6) - a(9)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 2030:
If b1(a(3)) = 0 Then GoTo 2030
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 2030
For j5 = m1 To m2 'a(5)
If b1(a1(j5)) = 0 Then GoTo 2050
If b(a1(j5)) = 0 Then b(a1(j5)) = a1(j5): c(5) = a1(j5) Else GoTo 2050
a(5) = a1(j5)
a(4) = s1 - a(5) - a(6)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 2040:
If b1(a(4)) = 0 Then GoTo 2040
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 2040
a(2) = s1 - a(5) - a(8)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 2020:
If b1(a(2)) = 0 Then GoTo 2020
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 2020
a(1) = -s1 + a(5) + a(6) + a(8) + a(9)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 2010:
If b1(a(1)) = 0 Then GoTo 2010
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 2010
GoSub 950: If fl1 = 0 Then GoTo 2005 ' Anti Symmetric
n10 = n10 + 1
If n10 <= 4 Then
GoSub 3000 ' Determine Adjacent Back Square
If fl2 = 0 Then
GoSub 905 ' Restore a(1) ... a(6) in b1()
n10 = n10 - 1: GoTo 2005
Else
GoSub 750 ' Transform and Assign Sub Squares to c6()
GoSub 910 ' Remove used primes a2() from b1()
End If
Erase b, c: GoTo 2090
Else
Erase b, c: GoTo 1000
End If
2005 b(c(1)) = 0: c(1) = 0
2010 b(c(2)) = 0: c(2) = 0
2020 b(c(4)) = 0: c(4) = 0
2040 b(c(5)) = 0: c(5) = 0
2050 Next j5
b(c(3)) = 0: c(3) = 0
2030 b(c(6)) = 0: c(6) = 0
2060 Next j6
b(c(7)) = 0: c(7) = 0
2070 b(c(8)) = 0: c(8) = 0
2080 Next j8
b(c(9)) = 0: c(9) = 0
2090 Next j9
1000 n10 = 0
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem6a")
End
' Determine Adjacent Back Square
3000 fl2 = 1
Erase b2, c2: GoSub 900 ' Remove a(1) ... a(6) from b1()
a2(9) = a(9): a2(8) = a(8): a2(7) = a(7)
b2(a2(9)) = a2(9): b2(a2(8)) = a2(8): b2(a2(7)) = a2(7):
For jj6 = m1 To m2 'a2(6)
If b1(a1(jj6)) = 0 Then GoTo 3060
If b2(a1(jj6)) = 0 Then b2(a1(jj6)) = a1(jj6): c2(6) = a1(jj6) Else GoTo 3060
a2(6) = a1(jj6)
a2(3) = s1 - a2(6) - a2(9)
If a2(3) < a1(m1) Or a2(3) > a1(m2) Then GoTo 3030:
If b1(a2(3)) = 0 Then GoTo 3030
If b2(a2(3)) = 0 Then b2(a2(3)) = a2(3): c2(3) = a2(3) Else GoTo 3030
For jj5 = m1 To m2 'a2(5)
If b1(a1(jj5)) = 0 Then GoTo 3050
If b2(a1(jj5)) = 0 Then b2(a1(jj5)) = a1(jj5): c2(5) = a1(jj5) Else GoTo 3050
a2(5) = a1(jj5)
a2(4) = s1 - a2(5) - a2(6)
If a2(4) < a1(m1) Or a2(4) > a1(m2) Then GoTo 3040:
If b1(a2(4)) = 0 Then GoTo 3040
If b2(a2(4)) = 0 Then b2(a2(4)) = a2(4): c2(4) = a2(4) Else GoTo 3040
a2(2) = s1 - a2(5) - a2(8)
If a2(2) < a1(m1) Or a2(2) > a1(m2) Then GoTo 3020:
If b1(a2(2)) = 0 Then GoTo 3020
If b2(a2(2)) = 0 Then b2(a2(2)) = a2(2): c2(2) = a2(2) Else GoTo 3020
a2(1) = -s1 + a2(5) + a2(6) + a2(8) + a2(9)
If a2(1) < a1(m1) Or a2(1) > a1(m2) Then GoTo 3010:
If b1(a2(1)) = 0 Then GoTo 3010
If b2(a2(1)) = 0 Then b2(a2(1)) = a2(1): c2(1) = a2(1) Else GoTo 3010
GoSub 960: If fl1 = 0 Then GoTo 3005 ' Anti Symmetric
Return
3005 b2(c2(1)) = 0: c2(1) = 0
3010 b2(c2(2)) = 0: c2(2) = 0
3020 b2(c2(4)) = 0: c2(4) = 0
3040 b2(c2(5)) = 0: c2(5) = 0
3050 Next jj5
b2(c2(3)) = 0: c2(3) = 0
3030 b2(c2(6)) = 0: c2(6) = 0
3060 Next jj6
fl2 = 0
Return
' Transform and Assign Sub Squares to c6()
750
Select Case n10
Case 1:
c6(1) = a(7): c6(2) = a(8): c6(3) = a(9): 'Top
c6(7) = a(4): c6(8) = a(5): c6(9) = a(6):
c6(13) = a(1): c6(14) = a(2): c6(15) = a(3):
c6(37) = a2(4): c6(38) = a2(5): c6(39) = a2(6): 'Back
c6(73) = a2(1): c6(74) = a2(2): c6(75) = a2(3):
Case 2:
c6(4) = a(7): c6(5) = a(8): c6(6) = a(9): 'Top
c6(10) = a(4): c6(11) = a(5): c6(12) = a(6):
c6(16) = a(1): c6(17) = a(2): c6(18) = a(3):
c6(40) = a2(4): c6(41) = a2(5): c6(42) = a2(6): 'Back
c6(76) = a2(1): c6(77) = a2(2): c6(78) = a2(3):
Case 3:
c6(19) = a(1): c6(20) = a(2): c6(21) = a(3): 'Top
c6(25) = a(4): c6(26) = a(5): c6(27) = a(6):
c6(31) = a(7): c6(32) = a(8): c6(33) = a(9):
c6(114) = Pr3 - a2(1): c6(110) = Pr3 - a2(2): c6(111) = Pr3 - a2(3): 'Back
c6(150) = Pr3 - a2(4): c6(146) = Pr3 - a2(5): c6(147) = Pr3 - a2(6):
Case 4:
c6(22) = a(1): c6(23) = a(2): c6(24) = a(3): 'Top
c6(28) = a(4): c6(29) = a(5): c6(30) = a(6):
c6(34) = a(7): c6(35) = a(8): c6(36) = a(9):
c6(112) = Pr3 - a2(1): c6(113) = Pr3 - a2(2): c6(109) = Pr3 - a2(3): 'Back
c6(148) = Pr3 - a2(4): c6(149) = Pr3 - a2(5): c6(145) = Pr3 - a2(6):
'Bottom
c6(181) = Pr3 - c6(36): c6(182) = Pr3 - c6(32): c6(183) = Pr3 - c6(33):
c6(184) = Pr3 - c6(34): c6(185) = Pr3 - c6(35): c6(186) = Pr3 - c6(31):
c6(187) = Pr3 - c6(12): c6(188) = Pr3 - c6(8): c6(189) = Pr3 - c6(9):
c6(190) = Pr3 - c6(10): c6(191) = Pr3 - c6(11): c6(192) = Pr3 - c6(7):
c6(193) = Pr3 - c6(18): c6(194) = Pr3 - c6(14): c6(195) = Pr3 - c6(15):
c6(196) = Pr3 - c6(16): c6(197) = Pr3 - c6(17): c6(198) = Pr3 - c6(13):
c6(199) = Pr3 - c6(24): c6(200) = Pr3 - c6(20): c6(201) = Pr3 - c6(21):
c6(202) = Pr3 - c6(22): c6(203) = Pr3 - c6(23): c6(204) = Pr3 - c6(19):
c6(205) = Pr3 - c6(30): c6(206) = Pr3 - c6(26): c6(207) = Pr3 - c6(27):
c6(208) = Pr3 - c6(28): c6(209) = Pr3 - c6(29): c6(210) = Pr3 - c6(25):
c6(211) = Pr3 - c6(6): c6(212) = Pr3 - c6(2): c6(213) = Pr3 - c6(3):
c6(214) = Pr3 - c6(4): c6(215) = Pr3 - c6(5): c6(216) = Pr3 - c6(1):
'Front
c6(67) = Pr3 - c6(42): c6(68) = Pr3 - c6(38): c6(69) = Pr3 - c6(39):
c6(70) = Pr3 - c6(40): c6(71) = Pr3 - c6(41): c6(72) = Pr3 - c6(37):
c6(103) = Pr3 - c6(78): c6(104) = Pr3 - c6(74): c6(105) = Pr3 - c6(75):
c6(106) = Pr3 - c6(76): c6(107) = Pr3 - c6(77): c6(108) = Pr3 - c6(73):
c6(139) = Pr3 - c6(114): c6(140) = Pr3 - c6(110): c6(141) = Pr3 - c6(111):
c6(142) = Pr3 - c6(112): c6(143) = Pr3 - c6(113): c6(144) = Pr3 - c6(109):
c6(175) = Pr3 - c6(150): c6(176) = Pr3 - c6(146): c6(177) = Pr3 - c6(147):
c6(178) = Pr3 - c6(148): c6(179) = Pr3 - c6(149): c6(180) = Pr3 - c6(145):
GoSub 850 'Back Check Identical Numbers
If fl1 = 1 Then
' n9 = n9 + 1: GoSub 1750 'Print Cube
n9 = n9 + 1: GoSub 1740 'Print Selected Numbers
End If
End Select
Return
' Exclude solutions with identical numbers c6()
850 fl1 = 1
For j1 = 1 To 216
a20 = c6(j1): If a20 = 0 Then GoTo 855
For j2 = (1 + j1) To 216
If a20 = c6(j2) Then fl1 = 0: Return
Next j2
855 Next j1
Return
' Remove primes a(1) ... a(6) from primes b1()
900 For i1 = 1 To 6
b1(a(i1)) = 0: b1(Pr3 - a(i1)) = 0
Next i1
Return
' Restore primes a(1) ... a(6) in b1()
905 For i1 = 1 To 6
b1(a(i1)) = a(i1): b1(Pr3 - a(i1)) = Pr3 - a(i1)
Next i1
Return
' Remove used primes a2() from available primes b1()
910 For i1 = 1 To 9
b1(a2(i1)) = 0: b1(Pr3 - a2(i1)) = 0
Next i1
Return
' Check Pairs a()
950 fl1 = 1: n25 = 0
For j1 = 1 To 9
a20 = Pr3 - a(j1) 'Complement
For j2 = (1 + j1) To 9
If a20 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Check Pairs a2()
960 fl1 = 1: n25 = 0
For j1 = 1 To 9
a20 = Pr3 - a2(j1) 'Complement
For j2 = (1 + j1) To 9
If a20 = a2(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Print Intrmediate Results
1740 For i1 = 1 To 216
Cells(n9, i1).Value = c6(i1)
Next i1
Cells(n9, 217).Value = s2
Cells(n9, 218).Value = j100
Return
' Print results (6 plane format)
1750 n2 = n2 + 1
If n2 = 4 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 = "MC = " + CStr(s2)
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)
Next i2
Next i1
Next i0
Return
' Read Prime Numbers From Sheet ShtNm1
3100 Pr3 = Sheets(ShtNm1).Cells(j100, 1).Value 'Pair Sum
s1 = 3 * Pr3 / 2 'MC3
s2 = 3 * Pr3 'MC6
nVar = Sheets(ShtNm1).Cells(j100, 5).Value
nSemi3 = Sheets(ShtNm1).Cells(j100, 6).Value 'Expected Nmbr Semi Magic Squares
m1 = 1: m2 = nVar
For i1 = m1 To m2
a1(i1) = Sheets(ShtNm1).Cells(j100, i1 + 10).Value
Next i1
If a1(1) = 1 Then m1 = 2
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
End Sub
