' Generates Magic Squares of order 4 for Odd Numbers
' Suitable as Diamond Inlays (L. S. Frierson)
' Tested with Office 365 under Windows 10
Sub Priem4d2()
Dim a1(81), a(16), b1(81), b(81), c(16), b3(81)
y = MsgBox("Locked", vbCritical, "Routine Priem4d2")
End
n2 = 0: n3 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
' Define variables
s1 = 164: nvar1 = 81
For i1 = 1 To nvar1
a1(i1) = i1
Next i1
m1 = 1: m2 = nvar1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Generate squares
For j16 = m1 To m2 Step 2 'a(16)
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
For j15 = m1 To m2 Step 2 'a(15)
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
For j14 = m1 To m2 Step 2 'a(14)
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)
a(13) = s1 - a(14) - a(15) - a(16)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130
If b1(a(13)) = 0 Then GoTo 130
If CInt(a(13) / 2) = a(13) / 2 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j12 = m1 To m2 Step 2 'a(12)
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(11) = s1 - a(12) - a(15) - a(16)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 70
If b1(a(11)) = 0 Then GoTo 70
If CInt(a(11) / 2) = a(11) / 2 Then GoTo 70
a(10) = s1 - a(12) - a(14) - a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 70
If b1(a(10)) = 0 Then GoTo 70
If CInt(a(10) / 2) = a(10) / 2 Then GoTo 70
a(9) = s1 - a(10) - a(11) - a(12)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 70
If b1(a(9)) = 0 Then GoTo 70
If CInt(a(9) / 2) = a(9) / 2 Then GoTo 70
a(8) = 0.5 * s1 - a(9)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 70
If b1(a(8)) = 0 Then GoTo 70
a(7) = 0.5 * s1 - a(10)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70:
If b1(a(7)) = 0 Then GoTo 70
a(6) = 0.5 * s1 - a(11)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 70:
If b1(a(6)) = 0 Then GoTo 70
a(5) = 0.5 * s1 - a(12)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 70:
If b1(a(5)) = 0 Then GoTo 70
a(4) = 0.5 * s1 - a(13)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 70:
If b1(a(4)) = 0 Then GoTo 70
a(3) = 0.5 * s1 - a(14)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 70:
If b1(a(3)) = 0 Then GoTo 70
a(2) = 0.5 * s1 - a(15)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 70:
If b1(a(2)) = 0 Then GoTo 70
a(1) = 0.5 * s1 - a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 70:
If b1(a(1)) = 0 Then GoTo 70
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 70
' Check Frierson Properties
GoSub 900: If fl1 = 0 Then GoTo 70
n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
' n9 = n9 + 1: GoSub 650 'Print results (squares)
' n9 = n9 + 1: Cells(1, 1).Value = n9 'Counting
70 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(16)) = 0: c(16) = 0
160 Next j16
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem4d2")
End
' Check Frierson Properties
900 fl1 = 1
' Around Hor Axes
x1 = a(9) Mod 10: x2 = a(14) Mod 10: If x1 <> x2 Then fl1 = 0: Return
x1 = a(5) Mod 10: x2 = a(15) Mod 10: If x1 <> x2 Then fl1 = 0: Return
x1 = a(1) Mod 10: x2 = a(16) Mod 10: If x1 <> x2 Then fl1 = 0: Return
x1 = a(6) Mod 10: x2 = a(11) Mod 10: If x1 <> x2 Then fl1 = 0: Return
x1 = a(2) Mod 10: x2 = a(12) Mod 10: If x1 <> x2 Then fl1 = 0: Return
x1 = a(3) Mod 10: x2 = a(8) Mod 10: If x1 <> x2 Then fl1 = 0: Return
' Around Vert Axes
x1 = a(5) + a(2): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
x1 = a(9) + a(3): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
x1 = a(13) + a(4): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
x1 = a(10) + a(7): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
x1 = a(14) + a(8): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
x1 = a(15) + a(12): x2 = x1 Mod 10: If x2 <> 2 Then fl1 = 0: Return
Return
' Print results (selected numbers)
640 For i1 = 1 To 16
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 17).Value = n9
Cells(1, 18).Value = n9
Return
Erase b3
For i1 = 1 To 16
b3(a(i1)) = a(i1)
Next i1
i2 = 0
For i1 = 1 To 81
If b3(i1) <> 0 Then
i2 = i2 + 1
Cells(n9, i2 + 18).Value = b3(i1)
End If
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 5: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
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 4
For i2 = 1 To 4
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 16
a2 = a(j1)
For j2 = (1 + j1) To 16
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
