' Generates Unique Concentric Magic Squares of order 5
' Tested with Office 365 under Windows 10
Sub MgcSqr5d3()
Dim a1(25), a(25), b1(25), b(25), c(25)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr5d3")
End
k1 = 1: k2 = 1: n1 = 0: n2 = 0: n9 = 0
' Define variables
For i1 = 1 To 25
a1(i1) = i1
Next i1
a(13) = 13: b(13) = 0 'Block Center Element
For i1 = 1 To 25
b1(a1(i1)) = a1(i1)
Next i1
m1 = 1: m2 = 25: s1 = 65: p2 = 26
t1 = Timer
Sheets("Klad1").Select
' Generate Border
For j25 = m2 To m1 Step -1 'a(25)
If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 250
a(25) = a1(j25)
a(1) = p2 - 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 = j25 - 1 To m1 Step -1 '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(5) = p2 - a(21)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If a(5) > a(21) Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j24 = m2 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(4) = p2 - a(24)
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 j23 = j24 - 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(3) = p2 - a(23)
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(22) = s1 - a(21) - a(23) - a(24) - a(25)
If a(22) < a1(m1) Or a(22) > a1(m2) Then GoTo 220
If b1(a(22)) = 0 Then GoTo 220
If a(22) > a(23) Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(2) = p2 - a(22)
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 j20 = m2 To m1 Step -1 '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(16) = p2 - a(20)
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
For j15 = j20 - 1 To m1 Step -1 '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(11) = p2 - a(15)
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
a(10) = s1 - a(5) - a(15) - a(20) - a(25)
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(15) Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(6) = p2 - a(10)
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
For j19 = m1 To m2 'a(19) Center Square 3 x 3
If b(a1(j19)) = 0 Then b(a1(j19)) = a1(j19): c(19) = a1(j19) Else GoTo 190
a(19) = a1(j19)
a(7) = p2 - a(19)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70:
If b1(a(7)) = 0 Then GoTo 70
If a(7) > a(19) Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j18 = m1 To m2 '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(8) = p2 - a(18)
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(17) = 3 * s1 / 5 - a(18) - a(19)
If a(17) < a1(m1) Or a(17) > a1(m2) Then GoTo 170:
If b1(a(17)) = 0 Then GoTo 170
If a(17) > a(19) Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(9) = p2 - a(17)
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(19) Then GoTo 90
If a(9) > a(17) Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(14) = 4 * s1 / 5 - a(18) - 2 * 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
a(12) = p2 - a(14)
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
' 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)
' Erase b, c: GoTo 250 'Print only first square for j25
5
b(c(12)) = 0: c(12) = 0
120 b(c(14)) = 0: c(14) = 0
140 b(c(9)) = 0: c(9) = 0
90 b(c(17)) = 0: c(17) = 0
170 b(c(8)) = 0: c(8) = 0
80 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(7)) = 0: c(7) = 0
70 b(c(19)) = 0: c(19) = 0
190 Next j19
b(c(6)) = 0: c(6) = 0
60 b(c(10)) = 0: c(10) = 0
100 b(c(11)) = 0: c(11) = 0
110 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(16)) = 0: c(16) = 0
160 b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(2)) = 0: c(2) = 0
20 b(c(22)) = 0: c(22) = 0
220 b(c(3)) = 0: c(3) = 0
30 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(4)) = 0: c(4) = 0
40 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(5)) = 0: c(5) = 0
50 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(1)) = 0: c(1) = 0
10 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 MgcSqr5d3")
End
' Print results (selected numbers)
640 For i1 = 1 To 25
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 26).Value = n9
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(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 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 (Back Check)
800 fl1 = 1
For j1 = 1 To 25
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 25
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
End Sub
