' Generates Magic Squares of order 3 with even Corner Numbers
' Suitable as Square Inlays for Inlaid Lozenge Squares
' Tested with Office 2007 under Windows 7
Sub Priem3b()
Dim a1(25), a(9), b1(25), b(25), c(9), b3(25)
y = MsgBox("Locked", vbCritical, "Routine Priem3b")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
For i1 = 1 To 25
a1(i1) = i1: b1(i1) = i1
Next i1
m1 = 1: m2 = 25: s1 = 39
Sheets("Klad1").Select
For j9 = m1 + 1 To m2 - 1 Step 2 'a(9) even
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 Step 2 'a(8) odd
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 CInt(a(7) / 2) <> a(7) / 2 Then GoTo 110 'a(7) even
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 110:
If b1(a(7)) = 0 Then GoTo 110
a(6) = 4 * s1 / 3 - a(8) - 2 * a(9):
If CInt(a(6) / 2) = a(6) / 2 Then GoTo 110 'a(6) odd
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 110:
If b1(a(6)) = 0 Then GoTo 110
a(5) = s1 / 3:
If CInt(a(5) / 2) = a(5) / 2 Then GoTo 110 'a(5) odd
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 110:
If b1(a(5)) = 0 Then GoTo 110
a(4) = -2 * s1 / 3 + 1 * a(8) + 2 * a(9):
If CInt(a(4) / 2) = a(4) / 2 Then GoTo 110 'a(4) odd
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 110:
If b1(a(4)) = 0 Then GoTo 110
a(3) = -s1 / 3 + 1 * a(8) + 1 * a(9):
If CInt(a(3) / 2) <> a(3) / 2 Then GoTo 110 'a(3) even
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 110:
If b1(a(3)) = 0 Then GoTo 110
a(2) = 2 * s1 / 3 - a(8):
If CInt(a(2) / 2) = a(2) / 2 Then GoTo 110 'a(2) odd
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 110:
If b1(a(2)) = 0 Then GoTo 110
a(1) = 2 * s1 / 3 - a(9):
If CInt(a(1) / 2) <> a(1) / 2 Then GoTo 110 'a(1) even
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 110:
If b1(a(1)) = 0 Then GoTo 110
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 110
n10 = n10 + 1
n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
' n9 = n9 + 1: GoSub 650 'Print results (squares)
110 b(c(8)) = 0: c(8) = 0
120 Next j8
b(c(9)) = 0: c(9) = 0
160 Next j9
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem3b")
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 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
Cells(k1, k2 + 1).Value = n9
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): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 9
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
End Sub
