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' 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

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