' Generates One Way Bent Diagonal Magic Squares of order 5
' Tested with Office 365 under Windows 10
Sub BentDia51()
Dim a1(25), a(25), b1(25), b(25), c(25)
y = MsgBox("Locked", vbCritical, "Routine BentDia51")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 25: s1 = 65
' 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 j25 = m1 To m2 'a(25)
If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 250
a(25) = a1(j25)
For j19 = m1 To m2 'a(19)
If b(a1(j19)) = 0 Then b(a1(j19)) = a1(j19): c(19) = a1(j19) Else GoTo 190
a(19) = a1(j19)
For j13 = m1 To m2 'a(13)
If b(a1(j13)) = 0 Then b(a1(j13)) = a1(j13): c(13) = a1(j13) Else GoTo 130
a(13) = a1(j13)
For j7 = m1 To m2 'a(7)
If b(a1(j7)) = 0 Then b(a1(j7)) = a1(j7): c(7) = a1(j7) Else GoTo 70
a(7) = a1(j7)
a(1) = s1 - a(7) - a(13) - a(19) - a(25)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If b1(a(1)) = 0 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j21 = m1 To m2 'a(21)
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)
a(17) = s1 - a(21) - a(13) - a(7) - a(1)
If a(17) < a1(m1) Or a(17) > a1(m2) Then GoTo 170
If b1(a(17)) = 0 Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(9) = 0.2 * s1 - a(17) - 0.5 * a(21) + 0.5 * a(1) + a(25)
If a(9) < a1(m1) Or a(9) > a1(m2) Or CInt(a(9)) <> a(9) 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) = -0.4 * s1 + a(9) + a(17) + a(7) + a(19) - a(25)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(12) = -0.2 * s1 + a(21) + a(1)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(11) = -0.6 * s1 + a(9) + a(17) + a(7) + a(19)
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
For j3 = m1 To m2 'a(3)
If b(a1(j3)) = 0 Then b(a1(j3)) = a1(j3): c(3) = a1(j3) Else GoTo 30
a(3) = a1(j3)
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(23) = s1 - a(19) - a(15) - a(9) - a(3)
If a(23) < a1(m1) Or a(23) > a1(m2) Then GoTo 230
If b1(a(23)) = 0 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(14) = 0.8 * s1 - a(15) - a(9) - a(19)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
For j8 = m1 To m2 'a(8)
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(18) = -a(8) + a(15) + a(9) - a(13) + a(19)
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180
If b1(a(18)) = 0 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
For j2 = m1 To m2 'a(2)
If b(a1(j2)) = 0 Then b(a1(j2)) = a1(j2): c(2) = a1(j2) Else GoTo 20
a(2) = a1(j2)
a(22) = 0.2 * s1 - a(2) + a(13)
If a(22) < a1(m1) Or a(22) > a1(m2) Then GoTo 220
If b1(a(22)) = 0 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(4) = 0.4 * s1 - a(2) - a(3) - a(9) + a(21) + a(13) - a(19) + a(25)
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(24) = -0.2 * s1 + a(2) + a(15) + a(3) + a(9) - a(21) - a(13) + a(19) - a(25)
If a(24) < a1(m1) Or a(24) > a1(m2) Then GoTo 240
If b1(a(24)) = 0 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
For j10 = m1 To m2 'a(10)
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(20) = 1.4 * s1 - a(10) - a(15) - a(9) - a(17) - a(7) - a(19)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(16) = -0.4 * s1 + a(10) + a(8) + a(7) + a(13) - a(19)
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160
If b1(a(16)) = 0 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(6) = s1 - a(10) - a(8) - a(9) - a(7)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
' n9 = n9 + 1: GoSub 650 'Print results (squares)
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: Cells(1, 1).Value = n9
5
b(c(6)) = 0: c(6) = 0
60 b(c(16)) = 0: c(16) = 0
160 b(c(20)) = 0: c(20) = 0
200 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(24)) = 0: c(24) = 0
240 b(c(4)) = 0: c(4) = 0
40 b(c(22)) = 0: c(22) = 0
220 b(c(2)) = 0: c(2) = 0
20 Next j2
b(c(18)) = 0: c(18) = 0
180 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(14)) = 0: c(14) = 0
140 b(c(23)) = 0: c(23) = 0
230 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(3)) = 0: c(3) = 0
30 Next j3
b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 b(c(5)) = 0: c(5) = 0
50 b(c(9)) = 0: c(9) = 0
90 b(c(17)) = 0: c(17) = 0
170 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(1)) = 0: c(1) = 0
10 b(c(7)) = 0: c(7) = 0
70 Next j7
b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(19)) = 0: c(19) = 0
190 Next j19
b(c(25)) = 0: c(25) = 0
250 Next j25
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine BentDia51")
End
' Print results (selected numbers)
640 Cells(n9, 25).Select
For i1 = 1 To 25
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 6: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 6
End If
Cells(1, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s1) 'n10
i3 = 0
For i1 = 1 To 5
For i2 = 1 To 5
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers or out of range
800 fl1 = 1
For i1 = 1 To 25
a2 = a(i1): If a2 = 0 Then GoTo 805
For i2 = (1 + i1) To 25
If a2 = a(i2) Then fl1 = 0: Return
Next i2
805 Next i1
Return
End Sub
