' Constructs 7 x 7 Primme Number Associated Magic Squares composed of
' - 2 each Overlapping Magic Anti Symmetric Corner Squares of Order 4
' - 2 each Semi Magic Anti Symmetric Corner Squares of Order 3
' Tested with Office 2007 under Windows 7
Sub Priem3g()
Dim a1(653), a(16), b1(45000), b(45123), c(16), a7(49)
y = MsgBox("Locked", vbCritical, "Routine Priem3g")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
Sheets("Klad1").Select
t1 = Timer
' Generate Squares
For j100 = 2 To 129
' Read Anti Symmetric Square Order 4
For i1 = 1 To 16
a(i1) = Sheets("Solutions4").Cells(j100, i1).Value
Next i1
Pr7 = 2 * a(16) 'Pair Sum
MC7 = 7 * a(16)
Rcrd1 = Sheets("Solutions4").Cells(j100, 18).Value 'Record Nr in "Pairs7"
n10 = 1: GoSub 750 'Transform and Assign Sub Squares Order 4
Erase a
' Read Prime Numbers From Sheet ShtNm1
s1 = 3 * Pr7 / 2 'MC3
Cntr7 = Sheets(ShtNm1).Cells(Rcrd1, 6).Value
If Cntr7 <> a7(25) Then
y = MsgBox("Conflict in Data", vbCritical, "Read Prime Numbers")
End
End If
nVar1 = Sheets(ShtNm1).Cells(Rcrd1, 9).Value
' Read Prime Numbers From sheet ShtNm1
For i1 = 1 To nVar1
a1(i1) = Sheets(ShtNm1).Cells(Rcrd1, 9 + i1).Value
Next i1
m1 = 1: m2 = nVar1
If a1(1) = 1 Then m1 = 2: m2 = nVar1 - 1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Remove Primes used for Overlapping Sub Squares (4 x 4)
For i1 = 1 To 49
b1(a7(i1)) = 0
Next i1
' Search Anti Symmetric Square Order 3
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
GoSub 800: If fl1 = 0 Then GoTo 80 ' Check Identical Numbers
GoSub 950: If fl1 = 0 Then GoTo 80 ' Check Pairs
n10 = 2
GoSub 750 ' Load Square Nr 2
GoSub 850 ' Back Check identical numbers a7()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 650 ' Print results (squares 7 x 7)
End If
Erase b, c: n10 = 0: GoTo 10 ' Print only first square
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
Erase b, c
10 n10 = 0
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem3g")
End
' Print results (Squares 7 x 7)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(MC7)
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a7(i3)
Next i2
Next i1
Return
' Transform and Assign Sub Squares
750 Select Case n10
Case 1: 'Left Top (4 x 4)
a7(1) = a(1): a7(2) = a(2): a7(3) = a(3): a7(4) = a(4):
a7(8) = a(5): a7(9) = a(6): a7(10) = a(7): a7(11) = a(8):
a7(15) = a(9): a7(16) = a(10): a7(17) = a(11): a7(18) = a(12):
a7(22) = a(13): a7(23) = a(14): a7(24) = a(15): a7(25) = a(16):
'Right Bottom (4 x 4)
a7(26) = Pr7 - a7(24): a7(27) = Pr7 - a7(23): a7(28) = Pr7 - a7(22):
a7(32) = Pr7 - a7(18): a7(33) = Pr7 - a7(17): a7(34) = Pr7 - a7(16): a7(35) = Pr7 - a7(15):
a7(39) = Pr7 - a7(11): a7(40) = Pr7 - a7(10): a7(41) = Pr7 - a7(9): a7(42) = Pr7 - a7(8):
a7(46) = Pr7 - a7(4): a7(47) = Pr7 - a7(3): a7(48) = Pr7 - a7(2): a7(49) = Pr7 - a7(1):
Case 2: 'Right Top (3 x 3)
a7(5) = a(1): a7(6) = a(2): a7(7) = a(3):
a7(12) = a(4): a7(13) = a(5): a7(14) = a(6):
a7(19) = a(7): a7(20) = a(8): a7(21) = a(9):
'Left Bottom (3 x 3)
a7(29) = Pr7 - a7(21): a7(30) = Pr7 - a7(20): a7(31) = Pr7 - a7(19):
a7(36) = Pr7 - a7(14): a7(37) = Pr7 - a7(13): a7(38) = Pr7 - a7(12):
a7(43) = Pr7 - a7(7): a7(44) = Pr7 - a7(6): a7(45) = Pr7 - a7(5):
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 a7()
850 fl1 = 1
For j1 = 1 To 49
a2 = a7(j1)
For j2 = (1 + j1) To 49
If a2 = a7(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Check Pairs
950 fl1 = 1: n25 = 0
For j1 = 1 To 9
a2 = Pr7 - a(j1) 'Complement
For j2 = (1 + j1) To 9
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
