' Generates Two Way Bent Diagonal Magic Squares of order 4 (Axial Symmetric)
' Tested with Office 365 under Windows 10
Sub BentDia41()
Dim a1(16), a(16), b1(16), b(16), c(16)
y = MsgBox("Locked", vbCritical, "Routine BentDia41")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 16: s1 = 34
' Define Variables
For i1 = m1 To m2
a1(i1) = i1
b1(a1(i1)) = a1(i1)
Next i1
' Generate squares
Sheets("Klad1").Select
t1 = Timer
For j16 = m1 To m2 'a(16)
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
a(4) = 0.5 * s1 - a(16): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j15 = m1 To m2 'a(15)
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(3) = 0.5 * s1 - a(15): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j14 = m1 To m2 '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(2) = 0.5 * s1 - a(14): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
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 b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(1) = 0.5 * s1 - a(13): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j12 = m1 To m2 '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(8) = 0.5 * s1 - a(12): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j11 = m1 To m2 'a(11)
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)
a(7) = 0.5 * s1 - a(11): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(10) = a(11) - a(13) + a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(6) = 0.5 * s1 - a(10): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(9) = 2 * s1 - 2 * a(11) - a(12) - a(14) - a(15) - 2 * a(16)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(5) = 0.5 * s1 - a(9): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
5
b(c(5)) = 0: c(5) = 0
50 b(c(9)) = 0: c(9) = 0
90 b(c(6)) = 0: c(6) = 0
60 b(c(10)) = 0: c(10) = 0
100 b(c(7)) = 0: c(7) = 0
70 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(8)) = 0: c(8) = 0
80 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(1)) = 0: c(1) = 0
10 b(c(13)) = 0: c(13) = 0
130 b(c(2)) = 0: c(2) = 0
20 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(3)) = 0: c(3) = 0
30 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(4)) = 0: c(4) = 0
40 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 BentDia41")
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(1, 1).Value = n9
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
