' Generates Bordered Magic Cubes of order 8 (Prime Numbers)
' Part II: Anti Symmetric Composed Semi Magic Back Squares
' Tested with Office 2007 under Windows 7
Sub PrimeCubes8b()
Dim a1(1040), a(32), b1(19720), b(19720), c(32)
Dim lns4(4, 4)
y = MsgBox("Locked", vbCritical, "Routine PrimeCubes8b")
End
n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0: n10 = 0
Sht1 = "Pairs8b": Sht2 = "TopSqrs8"
Sheets("Klad1").Select
t1 = Timer
n11 = 2: n12 = 2 'start row : column
n4 = 0: i4 = 0: n41 = 4 'current square
For j100 = 1 To 4 * 32 'Square nr j100 current
n4 = n4 + 1: n12 = 2 + (n4 - 1) * 5: i4 = 0
For j1 = n11 To n11 + 3 'Row within square j100
For j2 = n12 To n12 + 3 'Column within square j100
i4 = i4 + 1
a(i4) = Sheets(Sht2).Cells(j1, j2).Value 'load square
Next j2
Next j1
Select Case n4
Case 1
rcrd1a = Sheets(Sht2).Cells(n11, n12 - 1)
GoSub 810 'Read Primes b1()
For i1 = 1 To 4: lns4(1, i1) = a(i1): Next i1
GoSub 900 'Remove Primes Top Square 1
Case 2
For i1 = 1 To 4: lns4(2, i1) = a(i1): Next i1
GoSub 900 'Remove Primes Top Square 2
Case 3
For i1 = 1 To 4: lns4(3, i1) = Pr4 - a(12 + i1): Next i1
GoSub 900 'Remove Primes Top Square 3
Case 4
For i1 = 1 To 4: lns4(4, i1) = Pr4 - a(12 + i1): Next i1
GoSub 900 'Remove Primes Top Square 4
GoSub 820 'Define a1()
For j200 = 1 To 4
GoSub 600 'Calculate Back Square j200
n9 = n9 + 1: GoSub 650 'Print Square j200 (Includes not possible)
If j200 < 4 Then GoSub 900 'Remove Primes Square j200
Next j200
End Select
If n4 = n41 Then n4 = 0: n11 = n11 + 5: n12 = 2
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine PrimeCubes8b")
End
' Generate Squares
600 n10 = 0: Erase a, b, c
For i1 = 1 To 4:
a(12 + i1) = lns4(j200, i1)
b(a(12 + i1)) = a(12 + i1)
b(Pr4 - a(12 + i1)) = Pr4 - a(12 + i1)
Next i1
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(28) = Pr4 - a(12): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
For j11 = m1 To m2 'a(11)
If b1(a1(j11)) = 0 Then GoTo 110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)
a(27) = Pr4 - a(11): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
For j10 = m1 To m2 'a(10)
If b1(a1(j10)) = 0 Then GoTo 100
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(9) = s1 - a(10) - a(11) - a(12)
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(26) = Pr4 - a(10): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(25) = Pr4 - a(9): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 80
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(4) = -s1 - a(8) + a(9) + a(10) + a(11) + a(13) + a(14) + a(15)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40
If b1(a(4)) = 0 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(24) = Pr4 - a(8): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(20) = Pr4 - a(4): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
For j7 = m1 To m2 'a(7)
If b1(a1(j7)) = 0 Then GoTo 70
If b(a1(j7)) = 0 Then b(a1(j7)) = a1(j7): c(7) = a1(j7) Else GoTo 70
a(7) = a1(j7)
a(3) = s1 - a(7) - a(11) - a(15)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 30
If b1(a(3)) = 0 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(23) = Pr4 - a(7): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(19) = Pr4 - a(3): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 60
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 60
a(6) = a1(j6)
a(5) = s1 - a(6) - a(7) - a(8)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(2) = s1 - a(6) - a(10) - a(14)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 20
If b1(a(2)) = 0 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = a(6) + a(7) + a(8) - a(9) - a(13)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If b1(a(1)) = 0 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
a(22) = Pr4 - a(6): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = Pr4 - a(5): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(18) = Pr4 - a(2): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(17) = Pr4 - a(1): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
Return
5
b(c(17)) = 0: c(17) = 0
170 b(c(18)) = 0: c(18) = 0
180 b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 Next j6
b(c(19)) = 0: c(19) = 0
190 b(c(23)) = 0: c(23) = 0
230 b(c(3)) = 0: c(3) = 0
30 b(c(7)) = 0: c(7) = 0
70 Next j7
b(c(20)) = 0: c(20) = 0
200 b(c(24)) = 0: c(24) = 0
240 b(c(4)) = 0: c(4) = 0
40 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(25)) = 0: c(25) = 0
250 b(c(26)) = 0: c(26) = 0
260 b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(27)) = 0: c(27) = 0
270 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(28)) = 0: c(28) = 0
280 b(c(12)) = 0: c(12) = 0
120 Next j12
Return
' Print results (selected numbers)
640 For i1 = 1 To 16
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 5: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s1) + ", " + CStr(j200)
i3 = 0
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 16
a2 = a(j1)
For j2 = (1 + j1) To 16
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Read Prime Numbers From sheet Sht1
810 Erase b1
Pr4 = Sheets(Sht1).Cells(rcrd1a, 1).Value
s1 = 2 * Pr4
nVar = Sheets(Sht1).Cells(rcrd1a, 5).Value
m1 = 1: m2 = nVar
For i1 = m1 To m2
x = Sheets(Sht1).Cells(rcrd1a, i1 + 6).Value
b1(x) = x
Next i1
pMax = Sheets(Sht1).Cells(rcrd1a, m2 + 6).Value
Return
' Define a1()
820 n10 = 0
For i1 = 1 To pMax
If b1(i1) > 0 Then
n10 = n10 + 1: a1(n10) = b1(i1)
End If
Next i1
m2 = n10: n10 = 0
Return
' Remove used primes from available primes
900 For i1 = 1 To 16
b1(a(i1)) = 0
b1(Pr4 - a(i1)) = 0 'Complement
Next i1
Return
End Sub
