' Generates Essential Different Borders for Eccentric Magic Squares of order 6 (21,6 hrs)
' Tested with Office 365 under Windows 10
Sub MgcSqr6e5()
Dim a1(20), a(36), b1(36), b(36), c(36)
Dim s20(72)
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("Ranges4b").Select
For j100 = 2 To 22146
Cells(1, 17).Value = j100
' Reset
Erase b, c, s20
For i1 = 1 To 36: b1(i1) = i1: Next i1
' Read and Exclude Center Range
For i1 = 1 To 16
x = Sheets("Ranges4b").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
For s2 = 3 To 71
s22 = Sheets("Ranges4a").Cells(j100, 16 + s2).Value
If s22 = 0 Then GoTo 2000
' Generate Borders
For j31 = m1 To m2 '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(32) = p2 - a(31)
If a(32) < a1(m1) Or a(32) > a1(m2) Then GoTo 320
If b1(a(32)) = 0 Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
For j26 = m1 To m2 'a(26)
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
a(25) = p2 - a(26)
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 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(5) = p2 - a(11)
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(6) = s1 - a(11) - s2 - a(26) - a(31)
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(12) = p2 - a(6)
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
' 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(1) = p2 - a(8)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If a(1) < a(8) Then GoTo 10 'Prevent Row/Clmn Permutations
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 j7 = j8 + 1 To m2 'Prevent Row/Clmn Permutations
If b(a1(j7)) = 0 Then b(a1(j7)) = a1(j7): c(7) = a1(j7) Else GoTo 70
a(7) = a1(j7)
a(2) = p2 - a(7)
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(7) Then GoTo 20 'Prevent Mirror (Axes)
If a(2) < a(8) Then GoTo 20 'Prevent Row/Clmn Permutations
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j20 = m1 To m2 'a(20)
If b(a1(j20)) = 0 Then b(a1(j20)) = a1(j20): c(20) = a1(j20) Else GoTo 200
a(20) = a1(j20)
a(19) = p2 - a(20)
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
a(14) = s1 - a(20) - a(26) - a(32) - a(8) - a(2)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If a(14) > a(20) Then GoTo 140 'Prevent Permutation a(14), a(20)
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = p2 - a(14)
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
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(4) = p2 - a(10)
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(9) = s1 - a(7) - a(8) - a(10) - a(11) - a(12)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If a(9) > a(10) Then GoTo 90 'Prevent Permutation a(9), a(10)
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(3) = p2 - a(9)
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
s20(s2) = s20(s2) + 1
' 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
5
b(c(3)) = 0: c(3) = 0
30 b(c(9)) = 0: c(9) = 0
90 b(c(4)) = 0: c(4) = 0
40 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(2)) = 0: c(2) = 0
20 b(c(7)) = 0: c(7) = 0
70 Next j7
b(c(1)) = 0: c(1) = 0
10 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(12)) = 0: c(12) = 0
120 b(c(6)) = 0: c(6) = 0
60 b(c(5)) = 0: c(5) = 0
50 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(25)) = 0: c(25) = 0
250 b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(32)) = 0: c(32) = 0
320 b(c(31)) = 0: c(31) = 0
310 Next j31
2000 Next s2
' Add n6(j100, s2)
For i1 = 1 To 72
Cells(j100, 16 + i1).Value = s20(i1)
Next i1
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)
Cells(k1, k2 + 2).Font.Color = -4165632
Cells(k1, k2 + 2).Value = s2
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
End Sub
' Summarize Eccentric Magic Squares 6 x 6
Sub EccSum6()
y = MsgBox("Blocked", vbCritical, "EccSum6")
End
Sheets("Ranges4b").Select
s22 = 0
For j100 = 2 To 22146
s21 = 0
For j200 = 19 To 87
n4 = Sheets("Ranges4a").Cells(j100, j200).Value
n6 = Sheets("Ranges4b").Cells(j100, j200).Value
n46 = n4 * n6
s21 = s21 + n46
Next j200
Sheets("Ranges4b").Cells(j100, 88).Value = s21
s22 = s22 + s21
Next j100
Sheets("Ranges4b").Cells(22147, 88).Value = s22
End
End Sub
