' Constructs 9 x 9 Composed Magic Squares for Prime Numbers (Part 2)
' Semi Magic Sub Squares, Optimized for Sophie Germain Primes
' Tested with Office 2007 under Windows 7
Sub Priem9b2()
Dim a1(1260), b1(174299), b(174299), c(36), a(9), a9(81)
y = MsgBox("Locked", vbCritical, "Routine Priem9b2")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs2"
Sheets("Klad1").Select
t1 = Timer
' Generate Squares
For j100 = 2 To 7
s3 = Sheets("Lines9").Cells(j100, 82).Value / 3 'MC3
Rcrd1a = Sheets("Lines9").Cells(j100, 83).Value 'Record
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
If nVar < 81 Then GoTo 1000
m1 = 1: m2 = nVar
For i1 = 1 To m2
a1(i1) = Sheets(ShtNm1).Cells(Rcrd1a, i1 + 9).Value
Next i1
' Extended Range
Erase b1
For i1 = 1 To 1055
x = Sheets("SG1").Cells(i1, 1).Value
b1(x) = x
Next i1
' Read Magic Center and Border Squares
' Asign to a9() and and Remove from b1()
For i1 = 1 To 81
a9(i1) = Sheets("Lines9").Cells(j100, i1).Value
b1(a9(i1)) = 0
Next i1
' Generate Semi Magic Sub Squares
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 155
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 155
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 135
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 135
a(8) = a1(j8)
a(7) = s3 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 130:
If b1(a(7)) = 0 Then GoTo 130
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 105
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 105
a(6) = a1(j6)
For j5 = m1 To m2 'a(5)
If b1(a1(j5)) = 0 Then GoTo 95
If b(a1(j5)) = 0 Then b(a1(j5)) = a1(j5): c(5) = a1(j5) Else GoTo 95
a(5) = a1(j5)
a(4) = s3 - a(5) - a(6)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 85:
If b1(a(4)) = 0 Then GoTo 85
a(3) = -a(6) + a(7) + a(8)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 85:
If b1(a(3)) = 0 Then GoTo 85
a(2) = s3 - a(5) - a(8)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 85:
If b1(a(2)) = 0 Then GoTo 85
a(1) = a(5) + a(6) - a(7)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 85:
If b1(a(1)) = 0 Then GoTo 85
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 85
n10 = n10 + 1
Select Case n10
Case 1
GoSub 750: GoSub 900 'Assign Sub Square 1, Remove used primes
Erase b, c: GoTo 155
Case 2
GoSub 750: GoSub 900 'Assign Sub Square 2, Remove used primes
Erase b, c: GoTo 155
Case 3
GoSub 750: GoSub 900 'Assign Sub Square 3, Remove used primes
Erase b, c: GoTo 155
Case 4
GoSub 750 'Assign Sub Square 4
GoSub 850 'Double Check Identical Integers
If fl1 = 1 Then
n9 = n9 + 1: GoSub 660 'Print Composed Squares
End If
Erase b, c: GoTo 1000 'Only four Sub Squares required, next j100
End Select
85 b(c(5)) = 0: c(5) = 0
95 Next j5
b(c(6)) = 0: c(6) = 0
105 Next j6
130 b(c(8)) = 0: c(8) = 0
135 Next j8
b(c(9)) = 0: c(9) = 0
155 Next j9
1000 n10 = 0
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem9b2")
End
' Print results (selected numbers)
640 Cells(n9, 9).Select
For i1 = 1 To 81
Cells(n9, i1).Value = a9(i1)
Next i1
Cells(n9, 82).Value = 3 * s3
Return
' Print results (squares 9 x 9)
660 n1 = n1 + 1
If n1 = 3 Then
n1 = 1: k1 = k1 + 10: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 10
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(3 * s3)
i3 = 0
For i1 = 1 To 9
For i2 = 1 To 9
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a9(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers a9()
850 fl1 = 1
For j1 = 1 To 81
a20 = a9(j1): If a20 = 0 Then GoTo 860
For j2 = (1 + j1) To 81
If a20 = a9(j2) Then fl1 = 0: Return
Next j2
860 Next j1
Return
' Assign Sub Squares
750 Select Case n10
Case 1: 'Left
a9(28) = a(1): a9(29) = a(2): a9(30) = a(3):
a9(37) = a(4): a9(38) = a(5): a9(39) = a(6):
a9(46) = a(7): a9(47) = a(8): a9(48) = a(9):
Case 2: 'Top
a9(4) = a(1): a9(5) = a(2): a9(6) = a(3):
a9(13) = a(4): a9(14) = a(5): a9(15) = a(6):
a9(22) = a(7): a9(23) = a(8): a9(24) = a(9):
Case 3: 'Right
a9(34) = a(1): a9(35) = a(2): a9(36) = a(3):
a9(43) = a(4): a9(44) = a(5): a9(45) = a(6):
a9(52) = a(7): a9(53) = a(8): a9(54) = a(9):
Case 4: 'Bottom
a9(58) = a(1): a9(59) = a(2): a9(60) = a(3):
a9(67) = a(4): a9(68) = a(5): a9(69) = a(6):
a9(76) = a(7): a9(77) = a(8): a9(78) = a(9):
End Select
Return
' Exclude solutions with identical numbers a()
800 fl1 = 1
For j1 = 1 To 9
a20 = a(j1)
For j2 = (1 + j1) To 9
If a20 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Remove used primes a() from available primes b1()
900 For i1 = 1 To 9
b1(a(i1)) = 0
Next i1
Return
End Sub
