' Calculate Possible Ranges for Center Squares of 6 x 6 Concentric Squares
' 18! / (10! * 8!) = 43758
' Check which ranges result in n4(i) Essential Different Magic Squares (22145, 510 sec.)
' Tested with Office 365 under Windows 10
Sub CntrSqr4()
Dim a1(16), a(16), b1(36), b(36), c(16)
y = MsgBox("Blocked", 0, "CntrSqr4")
End
Sheets("Klad1").Select
t1 = Timer
m1 = 1: m2 = 16: s1 = 74
For j101 = 1 To 18
a1(1) = j101: a1(16) = 37 - a1(1)
For j102 = j101 + 1 To 18
a1(2) = j102: a1(15) = 37 - a1(2)
For j103 = j102 + 1 To 18
a1(3) = j103: a1(14) = 37 - a1(3)
For j104 = j103 + 1 To 18
a1(4) = j104: a1(13) = 37 - a1(4)
For j105 = j104 + 1 To 18
a1(5) = j105: a1(12) = 37 - a1(5)
For j106 = j105 + 1 To 18
a1(6) = j106: a1(11) = 37 - a1(6)
For j107 = j106 + 1 To 18
a1(7) = j107: a1(10) = 37 - a1(7)
For j108 = j107 + 1 To 18
a1(8) = j108: a1(9) = 37 - a1(8)
' Check Square Possible
GoSub 1000: If n4 = 0 Then GoTo 1080
n9 = n9 + 1: Cells(1, 20).Value = n9
For i1 = 1 To 16
Cells(n9, i1).Value = a1(i1)
Next i1
Cells(n9, 17).Value = n4
1080 Next j108
1070 Next j107
1060 Next j106
1050 Next j105
1040 Next j104
1030 Next j103
1020 Next j102
1010 Next j101
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem4b")
End
' Check Square Possible
1000 fl1 = 1: n4 = 0
Erase b1
For i1 = 1 To 16
b1(a1(i1)) = a1(i1)
Next i1
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)
For j11 = j16 + 1 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)
For j6 = j11 + 1 To m2 'a(6)
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 60
a(6) = a1(j6)
a(1) = s1 - a(6) - a(11) - a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If a(1) < a(16) 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 j13 = j16 + 1 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 j10 = j16 + 1 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(7) = s1 - a(6) - a(10) - a(11)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If a(7) < a(16) 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(4) = s1 - a(7) - a(10) - a(13)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40
If a(4) < a(16) Then GoTo 40
If a(4) < a(13) 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 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(14) = s1 - a(13) - a(15) - a(16)
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
a(3) = s1 - a(7) - a(11) - a(15)
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(2) = s1 - a(1) - a(3) - a(4)
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 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(9) = s1 - 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 b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = s1 - a(4) - a(12) - a(16)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(5) = s1 - a(1) - a(9) - a(13)
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
n4 = n4 + 1
b(c(5)) = 0: c(5) = 0
50 b(c(8)) = 0: c(8) = 0
80 b(c(9)) = 0: c(9) = 0
90 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(4)) = 0: c(4) = 0
40 b(c(7)) = 0: c(7) = 0
70 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(1)) = 0: c(1) = 0
10 b(c(6)) = 0: c(6) = 0
60 Next j6
b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(16)) = 0: c(16) = 0
160 Next j16
Return
End Sub
