' Constructs 12 x 12 Composed Magic Squares for Prime Numbers (Part 2)
' Eight order 3 Semi Magic Border Squares
' Tested with Office 2007 under Windows 7
Sub Priem12b2()
Dim a1(1260), b1(187141), b(187141), c(36), a(9), a12(144)
y = MsgBox("Locked", vbCritical, "Routine Priem12b2")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Priem2"
Sheets("Klad1").Select
t1 = Timer
' Generate Squares
For j100 = 2 To 43
s3 = Sheets("Lines12").Cells(j100, 145).Value / 4 'MC3
m1 = Sheets("Lines12").Cells(j100, 146).Value
m2 = Sheets("Lines12").Cells(j100, 147).Value
For i1 = 1 To m2
a1(i1) = Sheets(ShtNm1).Cells(i1, 3).Value
Next i1
pmax = a1(m2)
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Read Magic Center and Border Square
' Assign to a12() and and Remove from b1()
Erase a12
For i1 = 1 To 144
a12(i1) = Sheets("Lines12").Cells(j100, i1).Value
b1(a12(i1)) = 0
Next i1
' Restore available pairs in a1()
Erase 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
' 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: GoSub 900 'Assign Sub Square 4, Remove used primes
Erase b, c: GoTo 155
Case 5
GoSub 750: GoSub 900 'Assign Sub Square 5, Remove used primes
Erase b, c: GoTo 155
Case 6
GoSub 750: GoSub 900 'Assign Sub Square 6, Remove used primes
Erase b, c: GoTo 155
Case 7
GoSub 750: GoSub 900 'Assign Sub Square 7, Remove used primes
Erase b, c: GoTo 155
Case 8
GoSub 750 'Assign Sub Square 8
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
' Not found
GoSub 850 'Double Check Identical Integers
If fl1 = 1 Then
n9 = n9 + 1: GoSub 660 'Print Composed Squares
End If
Erase b, c
1000 n10 = 0
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem12b2")
End
' Print results (selected numbers)
640 Cells(n9, 9).Select
For i1 = 1 To 144
Cells(n9, i1).Value = a12(i1)
Next i1
Cells(n9, 145).Value = 4 * s3
Return
' Print results (squares 12 x 12)
660 n1 = n1 + 1
If n1 = 2 Then
n1 = 1: k1 = k1 + 13: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 13
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(4 * s3)
i3 = 0
For i1 = 1 To 12
For i2 = 1 To 12
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a12(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers a12()
850 fl1 = 1
For j1 = 1 To 144
a20 = a12(j1): If a20 = 0 Then GoTo 860
For j2 = (1 + j1) To 144
If a20 = a12(j2) Then fl1 = 0: Return
Next j2
860 Next j1
Return
' Assign Sub Squares (Clockwise)
750 Select Case n10
Case 1: 'Top / Left
a12(4) = a(1): a12(5) = a(2): a12(6) = a(3):
a12(16) = a(4): a12(17) = a(5): a12(18) = a(6):
a12(28) = a(7): a12(29) = a(8): a12(30) = a(9):
Case 2: 'Top / Right
a12(7) = a(1): a12(8) = a(2): a12(9) = a(3):
a12(19) = a(4): a12(20) = a(5): a12(21) = a(6):
a12(31) = a(7): a12(32) = a(8): a12(33) = a(9):
Case 3: 'Right / Top
a12(46) = a(1): a12(47) = a(2): a12(48) = a(3):
a12(58) = a(4): a12(59) = a(5): a12(60) = a(6):
a12(70) = a(7): a12(71) = a(8): a12(72) = a(9):
Case 4: 'Left / Bottom
a12(82) = a(1): a12(83) = a(2): a12(84) = a(3):
a12(94) = a(4): a12(95) = a(5): a12(96) = a(6):
a12(106) = a(7): a12(107) = a(8): a12(108) = a(9):
Case 5: 'Bottom / Right
a12(115) = a(1): a12(116) = a(2): a12(117) = a(3):
a12(127) = a(4): a12(128) = a(5): a12(129) = a(6):
a12(139) = a(7): a12(140) = a(8): a12(141) = a(9):
Case 6: 'Bottom / Left
a12(112) = a(1): a12(113) = a(2): a12(114) = a(3):
a12(124) = a(4): a12(125) = a(5): a12(126) = a(6):
a12(136) = a(7): a12(137) = a(8): a12(138) = a(9):
Case 7: 'Left / Bottom
a12(73) = a(1): a12(74) = a(2): a12(75) = a(3):
a12(85) = a(4): a12(86) = a(5): a12(87) = a(6):
a12(97) = a(7): a12(98) = a(8): a12(99) = a(9):
Case 8: 'Left / Top
a12(37) = a(1): a12(38) = a(2): a12(39) = a(3):
a12(49) = a(4): a12(50) = a(5): a12(51) = a(6):
a12(61) = a(7): a12(62) = a(8): a12(63) = 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
