' Generates Magic Squares of order 4 for integers 1 thru 16
' Tested with Office 2007 under Windows 7
Sub MgcSqr4b()
Dim a(16), b(16), c(16)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr4b")
End
n2 = 0: n3 = 0: n9 = 0
m1 = 1: m2 = 16: s1 = 34
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j16 = m1 To m2 'a(16)
If b(j16) = 0 Then b(j16) = j16: c(16) = j16 Else GoTo 160
a(16) = j16
For j15 = m1 To m2 'a(15)
If b(j15) = 0 Then b(j15) = j15: c(15) = j15 Else GoTo 150
a(15) = j15
For j14 = m1 To m2 'a(14)
If b(j14) = 0 Then b(j14) = j14: c(14) = j14 Else GoTo 140
j13 = s1 - j14 - j15 - j16
If j13 <= 0 Or j13 > 16 Then GoTo 130 'a(13)
If b(j13) = 0 Then b(j13) = j13: c(13) = j13 Else GoTo 130
a(14) = j14
a(13) = j13
For j12 = m1 To m2 'a(12)
If b(j12) = 0 Then b(j12) = j12: c(12) = j12 Else GoTo 120
a(12) = j12
For j11 = m1 To m2 'a(11)
If b(j11) = 0 Then b(j11) = j11: c(11) = j11 Else GoTo 110
a(11) = j11
For j10 = m1 To m2 'a(10)
If b(j10) = 0 Then b(j10) = j10: c(10) = j10 Else GoTo 100
j9 = s1 - j10 - j11 - j12
If j9 <= 0 Or j9 > 16 Then GoTo 90 'a(9)
If b(j9) = 0 Then b(j9) = j9: c(9) = j9 Else GoTo 90
a(10) = j10
a(9) = j9
For j8 = m1 To m2 'a(8)
If b(j8) = 0 Then b(j8) = j8: c(8) = j8 Else GoTo 80
a(8) = j8
a(7) = a(8) - a(10) + a(12) - a(13) + a(16)
If a(7) <= 0 Or a(7) > 16 Then GoTo 70
a(6) = s1 - a(8) - a(11) - a(12) + a(13) - a(16)
If a(6) <= 0 Or a(6) > 16 Then GoTo 70
a(5) = -a(8) + a(10) + a(11)
If a(5) <= 0 Or a(5) > 16 Then GoTo 70
a(4) = s1 - a(7) - a(10) - a(13)
If a(4) <= 0 Or a(4) > 16 Then GoTo 70
a(3) = -s1 - a(8) + a(9) + 2 * a(10) + 2 * a(13) + a(14)
If a(3) <= 0 Or a(3) > 16 Then GoTo 70
a(2) = a(8) - a(9) - 2 * a(10) + a(15) + 2 * a(16)
If a(2) <= 0 Or a(2) > 16 Then GoTo 70
a(1) = a(8) + a(12) - a(13)
If a(1) <= 0 Or a(1) > 16 Then GoTo 70
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 70
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
70 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(11)) = 0: c(11) = 0
110 Next j11
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 MgcSqr4b")
End
' Print results (selected numbers)
640 For i1 = 1 To 16
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 5: k2 = 0
Else
If n9 > 1 Then k2 = k2 + 5
End If
Cells(k1 + 1, k2 + 1).Select
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: GoTo 850
Next j2
Next j1
850 Return
End Sub
