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' Generates 5 x 5 Semi Magic Squares of Squares
' Based on `5 x 5 Generators

' Tested with Office 2007 under Windows 7

Sub CnstrSqrs5()

Dim a(25), a0(5, 5), a1(5), a2(5), s(14)
Dim n(5, 2)
Dim a3(5, 5), a4(5, 5), a5(16), d1(5), d2(5)

y = MsgBox("Blocked", vbInformation, "CnstrSqrs5")
End

Sheets("Klad1").Select

n1 = 0: n9 = 0: k1 = 1: k2 = 1

ShtNm1 = "GenLns5"
ShtNm2 = "ScrSht5"

t1 = Timer

For j100 = 7049 To 7058
Sheets("Klad1").Cells(1, 1).Value = j100

i2 = 1: i3 = 0
For i1 = 1 To 25:
    i3 = i3 + 1: If i3 = 6 Then i3 = 1: i2 = i2 + 1
    a0(i2, i3) = Sheets(ShtNm1).Cells(j100, i1)
Next i1
s2 = Sheets(ShtNm1).Cells(j100, 27)

    Sheets(ShtNm2).Select
    Cells.Select: Selection.ClearContents
    Range("A1").Select
    
    GoSub 500               ' Prepare Scratch Sheet
    
    Sheets("Klad1").Select
        
    For j1 = n(1, 1) To n(1, 2)
    
    n10 = 5: Erase a
    For i1 = 1 To 5
        a1(i1) = Sheets(ShtNm2).Cells(j1, i1).Value
    Next i1
    For i1 = 1 To 5         ' First Line
        a(i1) = a1(i1)
    Next i1
    
    For j2 = n(2, 1) To n(2, 2)
    j300 = j2: GoSub 100: If fl1 = 0 Then GoTo 20
    
    For j3 = n(3, 1) To n(3, 2)
    j300 = j3: GoSub 100: If fl1 = 0 Then GoTo 30
    
    For j4 = n(4, 1) To n(4, 2)
    j300 = j4: GoSub 100: If fl1 = 0 Then GoTo 40
    
    For j5 = n(5, 1) To n(5, 2)
    j300 = j5: GoSub 100: If fl1 = 0 Then GoTo 50
    
       Nc9 = Nc9 + 1                        'Unchecked
    
'      Check Possible Diagonals
    
       GoSub 200: If fl1 = 0 Then GoTo 5    'Write Sets 'ScrSht5'
       GoSub 400: If n29 = 0 Then GoTo 5    'Check Valid Sets
      
'      n9 = n9 + 1: GoSub 750               'Print Semi Magic Squares
                                            'Related number of Magic Squares Shown (n29)
5
       n10 = n10 - 5
50     Next j5
       n10 = n10 - 5
40     Next j4
       n10 = n10 - 5
30     Next j3
       n10 = n10 - 5
20     Next j2
       n10 = n10 - 5
10     Next j1
    
1000 Next j100

t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
    y = MsgBox(t10, 0, "Routine CnstrSqrs5")
End
    
'   Construct Semi Bimagic Squares

100 fl1 = 1

    For i1 = 1 To 5
        a2(i1) = Sheets(ShtNm2).Cells(j300, i1).Value
    Next i1

    For i1 = 1 To 5
    a20 = a2(i1)
    For i2 = 1 To n10
        If a20 = a(i2) Then fl1 = 0: Return
    Next i2
    Next i1
    
    n10 = n10 + 5
    i2 = 0
    For i1 = n10 - 5 + 1 To n10
        i2 = i2 + 1
        a(i1) = a2(i2)
    Next i1

    Return
    
'   Check Possibility Diagonals

200 fl1 = 1

    i2 = 1: i3 = 0
    For i1 = 1 To 25:
         i3 = i3 + 1: If i3 = 6 Then i3 = 1: i2 = i2 + 1
         a3(i2, i3) = a(i1)
    Next i1

    i19 = 0
    For i11 = 1 To 5
    For i12 = 1 To 5
    If i12 = i11 Then GoTo 220
    For i13 = 1 To 5
    If i13 = i11 Or i13 = i12 Then GoTo 230
    For i14 = 1 To 5
    If i14 = i11 Or i14 = i12 Or i14 = i13 Then GoTo 240
    For i15 = 1 To 5
    If i15 = i11 Or i15 = i12 Or i15 = i13 Or i15 = i14 Then GoTo 250
    
    s12 = a3(1, i11) ^ 2 + a3(2, i12) ^ 2 + a3(3, i13) ^ 2 + a3(4, i14) ^ 2 + a3(5, i15) ^ 2
    If s12 <> s2 Then GoTo 250
    
    i19 = i19 + 1
    
    Sheets(ShtNm2).Cells(i19, 11).Value = a3(1, i11)
    Sheets(ShtNm2).Cells(i19, 12).Value = a3(2, i12)
    Sheets(ShtNm2).Cells(i19, 13).Value = a3(3, i13)
    Sheets(ShtNm2).Cells(i19, 14).Value = a3(4, i14)
    Sheets(ShtNm2).Cells(i19, 15).Value = a3(5, i15)

250 Next i15
240 Next i14
230 Next i13
220 Next i12
210 Next i11

    If i19 < 2 Then fl1 = 0: Return

    n19 = 0
    For j11 = 1 To i19
 
    n20 = 5: Erase a5
    For i1 = 1 To 5
        a1(i1) = Sheets(ShtNm2).Cells(j11, i1 + 10).Value
    Next i1
    For i1 = 1 To 5   'First Line
        a5(i1) = a1(i1)
    Next i1
    
    For j12 = j11 + 1 To i19
    j300 = j12: GoSub 300: If fl2 = 0 Then GoTo 120

'      Write Set Diagonals to 'ScrSht6'

       For i1 = 1 To 2
            
            n19 = n19 + 1
            For i2 = 1 To 5
                 Sheets(ShtNm2).Cells(n19, i2 + 20).Value = a5(i2 + (i1 - 1) * 5)
            Next i2
            Sheets(ShtNm2).Cells(n19, 9 + 20).Value = i1
            Sheets(ShtNm2).Cells(n19, 9 + 21).Value = i21
            Sheets(ShtNm2).Cells(n19, 9 + 22).Value = i22
       Next i1

       n20 = n20 - 5
120    Next j12
       n20 = n20 - 5
110    Next j11

       If n19 < 2 Then fl1 = 0

Return
    
'   Construct Magic Set Diagonals

300 fl2 = 1

    For i1 = 1 To 5
        a2(i1) = Sheets(ShtNm2).Cells(j300, i1 + 10).Value
    Next i1

    n22 = 0
    For i1 = 1 To 5
    a20 = a2(i1)
    For i2 = 1 To n20
        If a20 = a5(i2) Then n22 = n22 + 1: i21 = i1: i22 = i2
    Next i2
    Next i1
    If n22 <> 1 Then fl2 = 0: Return    'Only one common allowed
    
 '  One Element Common (Center) ok
    
    n20 = n20 + 5: i22 = i22 + 5
    i2 = 0
    For i1 = n20 - 5 + 1 To n20
        i2 = i2 + 1
        a5(i1) = a2(i2)
    Next i1

    Return
        
'   Read Diagonals for Final Check

400
    n29 = 0:
    For j20 = 1 To n19 - 1 Step 2
        
        For i1 = 1 To 5
            d1(i1) = Sheets(ShtNm2).Cells(j20, i1 + 20).Value
            d2(i1) = Sheets(ShtNm2).Cells(j20 + 1, i1 + 20).Value
        Next i1

        Erase a4
        For i1 = 1 To 5
        For i2 = 1 To 5
            If a3(i1, i2) = d1(i1) Then a4(i1, i2) = 1
            If a3(i1, i2) = d2(i1) Then a4(i1, i2) = 2
        Next i2
        Next i1

        GoSub 450      'Check if transformation is possible
        
        If fl1 = 1 Then
            n29 = n29 + 1
            
'           Print Semi Magic Squares
'           Required Transformation Highlighted
            n9 = n9 + 1: GoSub 650
        
        End If
        
    Next j20

    Return

'   Check if transformation is possible

450 fl1 = 1

    For i1 = 1 To 5                 'rows
        n21 = 0: i41 = 0: i42 = 0
        For i2 = 1 To 5             'clmns
            If a4(i1, i2) <> 0 Then
               n21 = n21 + 1
               If n21 = 1 Then i41 = i2 Else i42 = i2
            End If
        Next i2

        If i41 = 0 Or i42 = 0 Then GoTo 460
        
        For i3 = i1 + 1 To 5
            If a4(i3, i41) = 0 And a4(i3, i42) = 0 Then
                                     'continue
            Else
               If a4(i3, i41) = a4(i1, i42) And a4(i3, i42) = a4(i1, i41) Then
                  Exit For          'ok
               Else
                  fl1 = 0: Return   'no match
               End If
            End If
        Next i3
        
    Next i1

460 Return
        
'   Prepare Scratch Sheet

500

i9 = 0: n(1, 1) = 1

For i1 = 1 To 5
For i2 = 1 To 5
For i3 = 1 To 5
For i4 = 1 To 5
For i5 = 1 To 5

    s12 = a0(1, i1) ^ 2 + a0(2, i2) ^ 2 + a0(3, i3) ^ 2 + a0(4, i4) ^ 2 + a0(5, i5) ^ 2
    If s12 <> s2 Then GoTo 550
    
    i9 = i9 + 1
    Cells(i9, 1).Value = a0(1, i1)
    Cells(i9, 2).Value = a0(2, i2)
    Cells(i9, 3).Value = a0(3, i3)
    Cells(i9, 4).Value = a0(4, i4)
    Cells(i9, 5).Value = a0(5, i5)


550 Next i5
540 Next i4
530 Next i3
520 Next i2
    
    n(i1, 2) = i9: If i1 <> 5 Then n(i1 + 1, 1) = i9 + 1

510 Next i1

    n(5, 2) = i9
   
    Return
    
'   Print Semi Magic Squares
'   Required Transformation Highlighted

650 n2 = n2 + 1
    If n2 = 4 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 = Nc9 ''n9
    Cells(k1, k2 + 2).Value = n29
    
    Cells(k1, k2 + 4).Value = j20   'Semi Magic
    Cells(k1, k2 + 5).Value = j100  'Generator  Bimagic Lines
    
    i3 = 0
    For i1 = 1 To 5
        For i2 = 1 To 5
            i3 = i3 + 1
            Cells(k1 + i1, k2 + i2).Value = a(i3)
            
            Select Case a4(i1, i2)
               
                Case 1
                         
                    Range(Cells(k1 + i1, k2 + i2), Cells(k1 + i1, k2 + i2)).Select
                    With Selection.Interior
                        .Pattern = xlSolid
                        .PatternColorIndex = xlAutomatic
                        .ThemeColor = xlThemeColorDark1
                        .TintAndShade = -0.149998474074526
                        .PatternTintAndShade = 0
                    End With
                         
                Case 2
            
                    Range(Cells(k1 + i1, k2 + i2), Cells(k1 + i1, k2 + i2)).Select
                    With Selection.Interior
                        .Pattern = xlSolid
                        .PatternColorIndex = xlAutomatic
                        .ThemeColor = xlThemeColorAccent5
                        .TintAndShade = 0.599993896298105
                        .PatternTintAndShade = 0
                    End With
                    
                Case 0
            
            End Select
            
        Next i2
    Next i1
   
    Return
    
'   Print results (Semi Magic Squares)
'   Related number of Magic Squares Shown (n29)
    
750 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).Font.Color = -4165632
    Cells(k1, k2 + 1).Value = n9
    Cells(k1, k2 + 2).Value = n29
    
    Cells(k1, k2 + 5).Value = j100
    
    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
    
End Sub

Vorige Pagina About the Author