' Generates sets of Semi Magic Squares of order 3 (Seven Magic Lines, Distinct Prime Numbers)
' Tested with Office 2007 under Windows 7
Sub Priem3c()
Dim a1(591), a(9), b1(21803), b(21803), C(9)
y = MsgBox("Locked", vbCritical, "Routine Priem3c")
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 300
' Define variables
s1 = Sheets(ShtNm1).Cells(j10, 3).Value 'MC3
nVar1 = Sheets(ShtNm1).Cells(j10, 5).Value
' Read Prime Numbers From sheet ShtNm1
For i1 = 1 To nVar1
a1(i1) = Sheets(ShtNm1).Cells(j10, 6 + 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
n10 = n10 + 1
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
' Erase b, C: GoTo 10 'Print only first square
GoSub 900 'Remove used primes from available primes
Erase b, c: Goto 160
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 Priem3c")
End
' Print results (selected numbers)
640 Cells(n9, 9).Select
For i1 = 1 To 9
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n1 = n1 + 1
If n1 = 5 or n10 = 1 Then
n1 = 1: k1 = k1 + 4: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 4
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
If n10 = 1 Then
Cells(k1, k2 + 1).Value = CStr(n10) + " (MC = " + CStr(s1) + ")"
Else
Cells(k1, k2 + 1).Value = CStr(n10)
End If
i3 = 0
For i1 = 1 To 3
For i2 = 1 To 3
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers
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
' Remove used primes from available primes
900 For i1 = 1 To 9
b1(a(i1)) = 0
Next i1
Return
End Sub
