' Generates Two Way V-ZigZag Magic Squares of order 4
' Tested with Office 2007 under Windows 7
Sub ZigZag4()
Dim a1(172), a(16), b1(1013), b(1013), c(16)
y = MsgBox("Locked", vbCritical, "Routine ZigZag4")
End
n2 = 0: n3 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 2
' Define variables
GoSub 2000
' Generate squares
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
a(14) = 0.5 * s1 - a(16): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(13) = 0.5 * s1 - a(15): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
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 110
If b1(a(11)) = 0 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(10) = 0.5 * s1 - a(12): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = 0.5 * s1 - a(11): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 80
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(7) = -s1 + a(8) + 2 * a(12) + a(15) + a(16)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(4) = s1 - a(8) - a(12) - a(16)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40
If b1(a(4)) = 0 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = s1 - a(8) - a(12) - a(15)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 30
If b1(a(3)) = 0 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(6) = 0.5 * s1 - a(8): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = 0.5 * s1 - a(7): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(2) = 0.5 * s1 - a(4): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = 0.5 * s1 - a(3): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
' Erase b, c: GoTo 1000 'Print only first square
5
b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(3)) = 0: c(3) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(7)) = 0: c(7) = 0
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 b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(13)) = 0: c(13) = 0
130 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(14)) = 0: c(14) = 0
140 b(c(16)) = 0: c(16) = 0
160 Next j16
n10 = 0
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine ZigZag4")
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 = 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
' Determine Integers
2000
s1 = 34: nVar = 16
m1 = 1: m2 = nVar
Erase b1
For i1 = m1 To m2
a1(i1) = i1: b1(a1(i1)) = a1(i1)
Next i1
Return
End Sub
