' Generates Prime Number Bordered Magic Squares (9 x 9)
' Split Border Lines, Center Square order 5
' Tested with Office 2007 under Windows 7
Sub Priem9c()
Dim a1(2448), a(169), a9(81), b1(43300), b(43300), c(81)
y = MsgBox("Locked", vbCritical, "Routine Priem9c")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
ShtNm2 = "Lines5"
t1 = Timer
For j100 = 2 To 1358
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 27).Value
MC5 = Sheets(ShtNm2).Cells(j100, 26).Value
' Read Prime Numbers From Sheet ShtNm1
Pr3 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value 'PairSum
s1 = Sheets(ShtNm1).Cells(Rcrd1a, 5).Value 'MC3
Cntr3 = Sheets(ShtNm1).Cells(Rcrd1a, 6).Value 'Center Element
s5 = 5 * Cntr3 'MC5
s9 = 9 * Cntr3 'MC9
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
If nVar < 81 Then GoTo 1000
If MC5 <> s5 Then
y = MsgBox("Conflict in Data", vbCritical, "Read " + ShtNm2)
End
End If
Erase b1
For j1 = 1 To nVar
x = Sheets(ShtNm1).Cells(Rcrd1a, 9 + j1).Value
b1(x) = x
Next j1
pMax = Sheets(ShtNm1).Cells(Rcrd1a, 9 + nVar).Value
' Read Center Square 5 x 5
For i1 = 1 To 25
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n10 = 0: n53 = 25: GoSub 910 'Remove used primes from available primes
Erase a9
a9(21) = a(1): a9(22) = a(2): a9(23) = a(3): a9(24) = a(4): a9(25) = a(5):
a9(30) = a(6): a9(31) = a(7): a9(32) = a(8): a9(33) = a(9): a9(34) = a(10):
a9(39) = a(11): a9(40) = a(12): a9(41) = a(13): a9(42) = a(14): a9(43) = a(15):
a9(48) = a(16): a9(49) = a(17): a9(50) = a(18): a9(51) = a(19): a9(52) = a(20):
a9(57) = a(21): a9(58) = a(22): a9(59) = a(23): a9(60) = a(24): a9(61) = a(25):
Erase a
' Restore available pairs in 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
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
' Determine Magic Squares and Rectangles
GoSub 2000 'Determine 4 Corner Squares
If n10 < 4 Then GoTo 950
GoSub 3000 'Determine 4 Border Sections
If n10 < 8 Then GoTo 950
GoSub 800 'Double Check Identical Integers a9()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 650 'Print Composed Squares a9()
End If
950 Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem9c")
End
' Determine Corner Squares 3 x 3
2000 fl1 = 1
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 90
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)
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(7) = s1 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70:
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = 4 * s1 / 3 - a(8) - 2 * a(9):
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
a(5) = s1 / 3:
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) = -2 * s1 / 3 + a(8) + 2 * a(9):
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(3) = -s1 / 3 + a(8) + a(9):
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(2) = 2 * s1 / 3 - a(8):
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) = 2 * s1 / 3 - a(9):
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
n10 = n10 + 1
If n10 < 4 Then
GoSub 750 'Transform and Assign Corner Squares
n53 = 9: GoSub 910 'Remove used primes a() from available primes b1()
Erase b, c: GoTo 90
Else
GoSub 750 'Transform and Assign Corner Squares
n53 = 9: GoSub 910 'Remove used primes a() from available primes b1()
End If
If n10 = 4 Then Erase b, c: Return 'Only four squares required
5 b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(2) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(9)) = 0: c(9) = 0
90 Next j9
fl1 = 0
Return
' Determine Border Sections 2 x 3
3000 fl1 = 1
For j1 = m1 To m2 'a(1)
If b1(a1(j1)) = 0 Then GoTo 3010
If b(a1(j1)) = 0 Then b(a1(j1)) = a1(j1): c(1) = a1(j1) Else GoTo 3010
a(1) = a1(j1)
a(4) = Pr3 - a(1): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 3040
For j2 = m1 To m2 'a(2)
If b1(a1(j2)) = 0 Then GoTo 3020
If b(a1(j2)) = 0 Then b(a1(j2)) = a1(j2): c(2) = a1(j2) Else GoTo 3020
a(2) = a1(j2)
a(5) = Pr3 - a(2): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 3050
a(3) = s1 - a(2) - a(1)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 3030
If b1(a(3)) = 0 Then GoTo 3030
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 3030
a(6) = Pr3 - a(3): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 3060
n10 = n10 + 1
If n10 < 8 Then
GoSub 750 'Transform and Assign Border Sections
n53 = 6: GoSub 910 'Remove used primes a() from available primes b1()
Erase b, c: GoTo 3010
Else
GoSub 750 'Transform and Assign Border Sections
n53 = 6: GoSub 910 'Remove used primes a() from available primes b1()
End If
If n10 = 8 Then Erase b, c: Return 'Only four Border Sections required
b(c(6)) = 0: c(6) = 0
3060 b(c(3)) = 0: c(3) = 0
3030 b(c(5)) = 0: c(5) = 0
3050 b(c(2)) = 0: c(2) = 0
3020 Next j2
b(c(4)) = 0: c(4) = 0
3040 b(c(1)) = 0: c(1) = 0
3010 Next j1
fl1 = 0
Return
' Print results (squares)
650 n5 = n5 + 1
If n5 = 3 Then
n5 = 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 = "MC = " + CStr(s9)
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
' Transform and Assign Corner Squares and Border Sections
750 Select Case n10
Case 1: 'Square 1, Left Top
a9(1) = a(9): a9(2) = a(7): a9(3) = a(8):
a9(10) = a(3): a9(11) = a(1): a9(12) = a(2):
a9(19) = a(6): a9(20) = a(4):
Case 2: 'Square 2, Right Top
a9(7) = a(8): a9(8) = a(9): a9(9) = a(7):
a9(16) = a(2): a9(17) = a(3): a9(18) = a(1):
a9(26) = a(6): a9(27) = a(4):
Case 3: 'Square 3, Right Bottom
a9(62) = a(6): a9(63) = a(4):
a9(70) = a(8): a9(71) = a(9): a9(72) = a(7):
a9(79) = a(2): a9(80) = a(3): a9(81) = a(1):
Case 4: 'Square 4, Left Bottom
a9(55) = a(6): a9(56) = a(4):
a9(64) = a(9): a9(65) = a(7): a9(66) = a(8):
a9(73) = a(3): a9(74) = a(1): a9(75) = a(2):
Case 5: 'Section 1, 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):
Case 6: 'Section 2, Right
a9(35) = a(1): a9(36) = a(4):
a9(44) = a(2): a9(45) = a(5):
a9(53) = a(3): a9(54) = a(6):
Case 7: 'Section 3, Bottom
a9(67) = a(1): a9(68) = a(2): a9(69) = a(3):
a9(76) = a(4): a9(77) = a(5): a9(78) = a(6):
Case 8: 'Section 4, Left
a9(28) = a(1): a9(29) = a(4):
a9(37) = a(2): a9(38) = a(5):
a9(46) = a(3): a9(47) = a(6):
End Select
Return
' Double Check Identical Numbers a9()
800 fl1 = 1
For i1 = 1 To 81
a20 = a9(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 81
If a20 = a9(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Remove used primes a() from available primes b1(), Reassign Center Element
910 For i1 = 1 To n53
b1(a(i1)) = 0
Next i1
If n10 < 4 Then b1(Cntr3) = Cntr3 'Reassign Center Element
Return
End Sub
