' Generates Unique Borders for Concentric Magic Squares of order 6 (995 sec)
' Tested with Office 365 under Windows 10
Sub MgcSqr6e4()
Dim a1(20), a(36), b1(36), b(36), c(36)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr6e4")
End
k1 = 1: k2 = 1: n1 = 0: n2 = 0: n9 = 0
m1 = 1: m2 = 20: s1 = 111: p2 = 37
t1 = Timer
Sheets("Ranges4").Select
For j100 = 2 To 22146
Cells(1, 23).Value = j100
' Reset
Erase b, c
For i1 = 1 To 36: b1(i1) = i1: Next i1
' Read and Exclude Center Range
For i1 = 1 To 16
x = Sheets("Ranges4").Cells(j100, i1).Value
b1(x) = 0
Next i1
' Define Border Variables
i2 = 0
For i1 = 1 To 36
x = b1(i1)
If x <> 0 Then i2 = i2 + 1: a1(i2) = i1
Next i1
n9 = 0
' Generate Border
For j36 = m2 To m1 Step -1 'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a(36) = a1(j36)
a(1) = p2 - a(36)
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 j31 = j36 - 1 To m1 Step -1 'a(31)
If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 310
a(31) = a1(j31)
a(6) = p2 - a(31)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If a(6) > a(31) Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j35 = m2 To m1 Step -1 'a(35)
If b(a1(j35)) = 0 Then b(a1(j35)) = a1(j35): c(35) = a1(j35) Else GoTo 350
a(35) = a1(j35)
a(5) = p2 - a(35)
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
For j34 = j35 - 1 To m1 Step -1 'a(34)
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
a(4) = p2 - a(34)
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
For j33 = j34 - 1 To m1 Step -1 'a(33)
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(3) = p2 - a(33)
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(32) = s1 - a(31) - a(33) - a(34) - a(35) - a(36)
If a(32) < a1(m1) Or a(32) > a1(m2) Then GoTo 320
If b1(a(32)) = 0 Then GoTo 320
If a(32) > a(33) Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(2) = p2 - a(32)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 20
If b1(a(2)) = 0 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j30 = m2 To m1 Step -1 'a(30)
If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
a(30) = a1(j30)
a(25) = p2 - a(30)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
For j24 = j30 - 1 To m1 Step -1 'a(24)
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(19) = p2 - a(24)
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
For j18 = j24 - 1 To m1 Step -1 'a(18)
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 180
a(18) = a1(j18)
a(13) = p2 - a(18)
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(12) = s1 - a(6) - a(18) - a(24) - a(30) - a(36)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If a(12) > a(18) Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(7) = p2 - a(12)
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
' 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)
n9 = n9 + 1:
5
b(c(7)) = 0: c(7) = 0
70 b(c(12)) = 0: c(12) = 0
120 b(c(13)) = 0: c(13) = 0
130 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(19)) = 0: c(19) = 0
190 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(25)) = 0: c(25) = 0
250 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(2)) = 0: c(2) = 0
20 b(c(32)) = 0: c(32) = 0
320 b(c(3)) = 0: c(3) = 0
30 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(4)) = 0: c(4) = 0
40 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(5)) = 0: c(5) = 0
50 b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(6)) = 0: c(6) = 0
60 b(c(31)) = 0: c(31) = 0
310 Next j31
b(c(1)) = 0: c(1) = 0
10 b(c(36)) = 0: c(36) = 0
360 Next j36
Sheets("Ranges4").Cells(j100, 18).Value = n9
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr6e4")
End
' Print results (selected numbers)
640 For i1 = 1 To 36
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 37).Value = n9
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9 ''"MC = " + CStr(s1)
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers (Back Check)
800 fl1 = 1
For j1 = 1 To 36
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 36
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
End Sub
