' Generates Associated Magic Squares of order 6
' Composed of 4 Semi Magic Anti Symmetric Squares (7 Magic Lines)
' Tested with Office 2007 under Windows 7
Sub Priem3e2()
Dim a1(591), a(9), b1(21803), b(21803), c(9), a6(36)
y = MsgBox("Locked", vbCritical, "Routine Priem3e2")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs6" 'Pairs6, Pairs8 for 6 x 6 and 12 x 12
'Pairs3, Pairs7 for 9 x 9 and 15 x 15
Sheets("Klad1").Select
t1 = Timer
' Generate Squares
For j10 = 2 To 1393
' Define variables
Pr3 = Sheets(ShtNm1).Cells(j10, 1).Value 'Pair Sum
s1 = 3 * Pr3 / 2
MC6 = 2 * s1
nVar1 = Sheets(ShtNm1).Cells(j10, 5).Value
Cells(k1, 1).Select: Cells(k1, 1).Value = s1
' Read Prime Numbers From sheet ShtNm1
For i1 = 1 To nVar1
a1(i1) = Sheets(ShtNm1).Cells(j10, 10 + i1).Value
Next i1
m1 = 1: m2 = nVar1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Generate Squares
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 160
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 160
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 120
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 120
a(8) = a1(j8)
a(7) = s1 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 110:
If b1(a(7)) = 0 Then GoTo 110
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 100
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 100
a(6) = a1(j6)
a(5) = -s1 + a(6) + a(8) + 2 * a(9)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 80:
If b1(a(5)) = 0 Then GoTo 80
a(4) = 2 * s1 - 2 * a(6) - a(8) - 2 * a(9)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 80:
If b1(a(4)) = 0 Then GoTo 80
a(3) = s1 - a(6) - a(9)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 80:
If b1(a(3)) = 0 Then GoTo 80
a(2) = 2 * s1 - a(6) - 2 * a(8) - 2 * a(9)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 80:
If b1(a(2)) = 0 Then GoTo 80
a(1) = -2 * s1 + 2 * a(6) + 2 * a(8) + 3 * a(9)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 80:
If b1(a(1)) = 0 Then GoTo 80
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 80
GoSub 950: If fl1 = 0 Then GoTo 80 ' Check Pairs
n10 = n10 + 1
If n10 = 2 Then
GoSub 750 ' Load Square Nr 2
GoSub 850 ' Back Check identical numbers a6()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 650 ' Print results (squares 6 x 6)
End If
Erase b, c: n10 = 0: GoTo 10 ' Print only first square
Else
GoSub 750 ' Load Square Nr 1
GoSub 900 ' Remove used primes from available primes
Erase b, c: GoTo 160
End If
80 b(c(6)) = 0: c(6) = 0
100 Next j6
110 b(c(8)) = 0: c(8) = 0
120 Next j8
b(c(9)) = 0: c(9) = 0
160 Next j9
10 n10 = 0
Next j10
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem3e2")
End
' Print results (squares 6 x 6)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = MC6
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a6(i3)
Next i2
Next i1
Return
' Transform and Assign Sub Squares
750 Select Case n10
Case 1: 'Left Top
a6(1) = a(3): a6(2) = a(2): a6(3) = a(1):
a6(7) = a(6): a6(8) = a(5): a6(9) = a(4):
a6(13) = a(9): a6(14) = a(8): a6(15) = a(7):
'Right Bottom
a6(22) = Pr3 - a6(15): a6(23) = Pr3 - a6(14): a6(24) = Pr3 - a6(13):
a6(28) = Pr3 - a6(9): a6(29) = Pr3 - a6(8): a6(30) = Pr3 - a6(7):
a6(34) = Pr3 - a6(3): a6(35) = Pr3 - a6(2): a6(36) = Pr3 - a6(1):
Case 2: 'Right Top
a6(4) = a(1): a6(5) = a(2): a6(6) = a(3):
a6(10) = a(4): a6(11) = a(5): a6(12) = a(6):
a6(16) = a(7): a6(17) = a(8): a6(18) = a(9):
'Left Bottom
a6(19) = Pr3 - a6(18): a6(20) = Pr3 - a6(17): a6(21) = Pr3 - a6(16):
a6(25) = Pr3 - a6(12): a6(26) = Pr3 - a6(11): a6(27) = Pr3 - a6(10):
a6(31) = Pr3 - a6(6): a6(32) = Pr3 - a6(5): a6(33) = Pr3 - a6(4):
End Select
Return
' Exclude solutions with identical numbers a()
800 fl1 = 1
For j1 = 1 To 9
a2 = a(j1)
For j2 = (1 + j1) To 9
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Back Check identical numbers a6()
850 fl1 = 1
For j1 = 1 To 36
a2 = a6(j1)
For j2 = (1 + j1) To 36
If a2 = a6(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Remove used primes from available primes
900 For i1 = 1 To 9
b1(a(i1)) = 0: b1(Pr3 - a(i1)) = 0
Next i1
Return
' Check Pairs
950 fl1 = 1: n25 = 0
For j1 = 1 To 9
a2 = Pr3 - a(j1) 'Complement
For j2 = (1 + j1) To 9
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
