' Constructs 9 x 9 Composed Magic Squares for Prime Numbers (Part 1)
' Semi Magic Sub Squares, Optimized for Sophie Germain Primes
' Tested with Office 2007 under Windows 7
Sub Priem9b1()
Dim a1(1260), b1(174299), b(174299), c(36), a(36), a9(81)
y = MsgBox("Locked", vbCritical, "Routine Priem9b1")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs2"
Sheets("Klad1").Select
t1 = Timer
' Generate Squares
For j100 = 5 To 11
s3 = Sheets("Lines3").Cells(j100, 10).Value 'MC3
s6 = 2 * s3
Rcrd1a = Sheets("Lines3").Cells(j100, 11).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 Square and Remove from b1()
For i1 = 1 To 9
a(i1) = Sheets("Lines3").Cells(j100, i1).Value
b1(a(i1)) = 0
Next i1
' Assign to a9()
n10 = 5: GoSub 750: n10 = 0
Erase a
' Generate Corner Squares
For j31 = m1 To m2 / 2 'a(31) Main Diagonal
If b1(a1(j31)) = 0 Then GoTo 310
If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 310
a(31) = a1(j31)
For j26 = m1 To m2 'a(26)
If b1(a1(j26)) = 0 Then GoTo 260
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
For j21 = m1 To m2 'a(21)
If b1(a1(j21)) = 0 Then GoTo 210
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)
For j32 = m1 To m2 'a(32) Square 1
If b1(a1(j32)) = 0 Then GoTo 320
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)
a(33) = s6 / 2 - a(31) - a(32)
If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
If b1(a(33)) = 0 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(27) = -a(21) + a(31) + a(32)
If a(27) < a1(m1) Or a(27) > a1(m2) Then GoTo 270
If b1(a(27)) = 0 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(25) = s6 / 2 + a(21) - a(26) - a(31) - a(32)
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(20) = s6 / 2 - a(26) - a(32)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = -a(21) + a(26) + a(32)
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
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
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(6) = s6 - a(11) - a(16) - a(21) - a(26) - a(31)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j17 = m1 To m2 'a(17) Square 2
If b1(a1(j17)) = 0 Then GoTo 170
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)
a(18) = s6 / 2 - a(16) - a(17)
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180
If b1(a(18)) = 0 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(12) = -a(6) + a(16) + a(17)
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(10) = s6 / 2 + a(6) - a(11) - a(16) - a(17)
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(5) = s6 / 2 - a(11) - a(17)
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(4) = -a(6) + a(11) + a(17)
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
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 5
n10 = n10 + 1
Select Case n10
Case 1
GoSub 750 'Assign Sub Squares 1, 2
GoSub 900 'Remove used primes
Erase b, c: GoTo 310
Case 2
GoSub 750 'Assign Sub Squares 3, 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
5
b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(10)) = 0: c(10) = 0
100 b(c(12)) = 0: c(12) = 0
120 b(c(18)) = 0: c(18) = 0
180 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(6)) = 0: c(6) = 0
60 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(16)) = 0: c(16) = 0
160 Next j16
b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(25)) = 0: c(25) = 0
250 b(c(27)) = 0: c(27) = 0
270 b(c(33)) = 0: c(33) = 0
330 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(31)) = 0: c(31) = 0
310 Next j31
1000 n10 = 0
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem9b1")
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
'Top / Right
a9(7) = a(4): a9(8) = a(5): a9(9) = a(6):
a9(16) = a(10): a9(17) = a(11): a9(18) = a(12):
a9(25) = a(16): a9(26) = a(17): a9(27) = a(18):
'Bottom / Left
a9(55) = a(19): a9(56) = a(20): a9(57) = a(21):
a9(64) = a(25): a9(65) = a(26): a9(66) = a(27):
a9(73) = a(31): a9(74) = a(32): a9(75) = a(33):
Case 2
'Top / Left
a9(1) = a(6): a9(2) = a(5): a9(3) = a(4):
a9(10) = a(12): a9(11) = a(11): a9(12) = a(10):
a9(19) = a(18): a9(20) = a(17): a9(21) = a(16):
'Bottom / Right
a9(61) = a(21): a9(62) = a(20): a9(63) = a(19):
a9(70) = a(27): a9(71) = a(26): a9(72) = a(25):
a9(79) = a(33): a9(80) = a(32): a9(81) = a(31):
Case 5: 'Center
a9(31) = a(1): a9(32) = a(2): a9(33) = a(3):
a9(40) = a(4): a9(41) = a(5): a9(42) = a(6):
a9(49) = a(7): a9(50) = a(8): a9(51) = a(9):
End Select
Return
' Exclude solutions with identical numbers a()
800 fl1 = 1
For j1 = 1 To 36
a20 = a(j1): If a20 = 0 Then GoTo 810
For j2 = (1 + j1) To 36
If a20 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
' Remove used primes a() from available primes b1()
900 For i1 = 1 To 36
b1(a(i1)) = 0
Next i1
Return
End Sub
