' Generates Unique 'Borders' for Eccentric Magic Squares of order 7
' Tested with Office 2007 under Windows 7
Sub MgcSqr7e2()
Dim a1(24), a(49), b1(49), b(49), c(49)
y = MsgBox("Locked", vbCritical, "Routine Priem7c")
End
k1 = 1: k2 = 1: n1 = 0: n2 = 0: n9 = 0
' Define variables
a1(1) = 1: a1(2) = 2: a1(3) = 3: a1(4) = 4: a1(5) = 5: a1(6) = 6:
a1(7) = 7: a1(8) = 8: a1(9) = 9: a1(10) = 10: a1(11) = 11: a1(12) = 12:
a1(13) = 38: a1(14) = 39: a1(15) = 40: a1(16) = 41: a1(17) = 42: a1(18) = 43:
a1(19) = 44: a1(20) = 45: a1(21) = 46: a1(22) = 47: a1(23) = 48: a1(24) = 49:
For i1 = 1 To 24
b1(a1(i1)) = a1(i1)
Next i1
m1 = 1: m2 = 24: s1 = 175: p2 = 50
t1 = Timer
Sheets("Klad1").Select
For j100 = 2 To 68
s2 = Sheets("Enum7").Cells(j100, 1).Value
Cells(j100, 1).Select
If s2 = 0 Then GoTo 1000
' Diagonal a(7) ... a(43)
n9 = 0
For j43 = m1 To m2 'a(43)
If b(a1(j43)) = 0 Then b(a1(j43)) = a1(j43): c(43) = a1(j43) Else GoTo 430
a(43) = a1(j43)
a(44) = p2 - a(43)
If a(44) < a1(m1) Or a(44) > a1(m2) Then GoTo 440
If b1(a(44)) = 0 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
For j37 = m1 To m2 'a(37)
If b(a1(j37)) = 0 Then b(a1(j37)) = a1(j37): c(37) = a1(j37) Else GoTo 370
a(37) = a1(j37)
a(36) = p2 - a(37)
If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 360
If b1(a(36)) = 0 Then GoTo 360
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
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)
a(6) = p2 - a(13)
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
a(7) = s1 - a(13) - s2 - a(37) - a(43)
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(14) = p2 - a(7)
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
' Left Corner
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(2) = p2 - a(8)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 20
If b1(a(2)) = 0 Then GoTo 20
If a(2) > a(8) Then GoTo 20 'Prevent Mirror (Axes)
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j9 = m1 To m2 'a(9)
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)
a(1) = p2 - a(9)
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
' Remainder Border
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(29) = p2 - a(30)
If a(29) < a1(m1) Or a(29) > a1(m2) Then GoTo 290
If b1(a(29)) = 0 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
For j23 = j30 - 1 To m1 Step -1 'a(23)
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
a(22) = p2 - a(23)
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(16) = s1 - a(44) - a(37) - a(30) - a(23) - a(9) - a(2)
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160
If b1(a(16)) = 0 Then GoTo 160
If a(16) > a(23) Then GoTo 160 'Prevent Permutation
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(15) = p2 - a(16)
If a(15) < a1(m1) Or a(15) > a1(m2) Then GoTo 150
If b1(a(15)) = 0 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j12 = m2 To m1 Step -1 '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(5) = p2 - a(12)
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 j11 = j12 - 1 To m1 Step -1 '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(4) = p2 - a(11)
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(10) = s1 - a(14) - a(13) - a(12) - a(11) - a(9) - a(8)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If a(10) > a(11) Then GoTo 100 'Prevent Permutation
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(3) = p2 - a(10)
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
' 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: Cells(j100, 2).Value = n9 'Counting
' Erase b, c: GoTo 430 'Print only first square for j43
5
b(c(3)) = 0: c(3) = 0
30 b(c(10)) = 0: c(10) = 0
100 b(c(4)) = 0: c(4) = 0
40 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(5)) = 0: c(5) = 0
50 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(15)) = 0: c(15) = 0
150 b(c(16)) = 0: c(16) = 0
160 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(1)) = 0: c(1) = 0
10 b(c(9)) = 0: c(9) = 0
90 Next j9
b(c(2)) = 0: c(2) = 0
20 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(14)) = 0: c(14) = 0
140 b(c(7)) = 0: c(7) = 0
70 b(c(6)) = 0: c(6) = 0
60 b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 Next j37
b(c(44)) = 0: c(44) = 0
440 b(c(43)) = 0: c(43) = 0
430 Next j43
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem7c")
End
' Print results (selected numbers)
640 For i1 = 1 To 49
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 50).Value = n9
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9 ''"MC = " + CStr(s1)
Cells(k1, k2 + 2).Font.Color = -4165632
Cells(k1, k2 + 2).Value = s2
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
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 49
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 49
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
End Sub
