' Generates Semi Bimagic Squares of order 6
' Bimagic Rows and Columns, Resulting Bimagic Diagonals
' Based on `6 x 6 Generators
' Tested with Office 2007 under Windows 7
Sub CnstrSqrs6133()
Dim a(36), a0(6, 6), a1(6), a2(6), s(14)
Dim n(6, 2)
Dim a3(6, 6), a4(6, 6), a5(16), d1(6), d2(6)
y = MsgBox("Blocked", vbInformation, "CnstrSqrs6133")
End
Sheets("Klad1").Select
n1 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "GenLns6d"
ShtNm2 = "ScrSht6"
t1 = Timer
For j100 = 1 To 5
i2 = 1: i3 = 0
For i1 = 1 To 36:
i3 = i3 + 1: If i3 = 7 Then i3 = 1: i2 = i2 + 1
a0(i2, i3) = Sheets(ShtNm1).Cells(j100, i1)
Next i1
s1 = Sheets(ShtNm1).Cells(j100, 38)
s2 = Sheets(ShtNm1).Cells(j100, 39)
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 = 6: Erase a
For i1 = 1 To 6
a1(i1) = Sheets(ShtNm2).Cells(j1, i1).Value
Next i1
For i1 = 1 To 6 ' 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
For j6 = n(6, 1) To n(6, 2)
j300 = j6: GoSub 100: If fl1 = 0 Then GoTo 60
Nc9 = Nc9 + 1 'Unchecked
' Check Possible Diagonals
GoSub 200: If fl1 = 0 Then GoTo 5 'Write Sets 'ScrSht6'
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 - 6
60 Next j6
n10 = n10 - 6
50 Next j5
n10 = n10 - 6
40 Next j4
n10 = n10 - 6
30 Next j3
n10 = n10 - 6
20 Next j2
n10 = n10 - 6
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 CnstrSqrs6133")
End
' Construct Semi Bimagic Squares
100 fl1 = 1
For i1 = 1 To 6
a2(i1) = Sheets(ShtNm2).Cells(j300, i1).Value
Next i1
For i1 = 1 To 6
a20 = a2(i1)
For i2 = 1 To n10
If a20 = a(i2) Then fl1 = 0: Return
Next i2
Next i1
n10 = n10 + 6
i2 = 0
For i1 = n10 - 6 + 1 To n10
i2 = i2 + 1
a(i1) = a2(i2)
Next i1
Return
' Check Possibility Diagonals (Bimagic)
200 fl1 = 1
i2 = 1: i3 = 0
For i1 = 1 To 36:
i3 = i3 + 1: If i3 = 7 Then i3 = 1: i2 = i2 + 1
a3(i2, i3) = a(i1)
Next i1
i19 = 0
For i11 = 1 To 6
For i12 = 1 To 6
If i12 = i11 Then GoTo 220
For i13 = 1 To 6
If i13 = i11 Or i13 = i12 Then GoTo 230
For i14 = 1 To 6
If i14 = i11 Or i14 = i12 Or i14 = i13 Then GoTo 240
For i15 = 1 To 6
If i15 = i11 Or i15 = i12 Or i15 = i13 Or i15 = i14 Then GoTo 250
For i16 = 1 To 6
If i16 = i11 Or i16 = i12 Or i16 = i13 Or i16 = i14 Or i16 = i15 Then GoTo 260
s11 = a3(1, i11) + a3(2, i12) + a3(3, i13) + a3(4, i14) + a3(5, i15) + a3(6, i16)
If s11 <> s1 Then GoTo 260
s12 = a3(1, i11) ^ 2 + a3(2, i12) ^ 2 + a3(3, i13) ^ 2 + a3(4, i14) ^ 2 + a3(5, i15) ^ 2 + a3(6, i16) ^ 2
If s12 <> s2 Then GoTo 260
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)
Sheets(ShtNm2).Cells(i19, 16).Value = a3(6, i16)
260 Next i16
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 = 6: Erase a5
For i1 = 1 To 6
a1(i1) = Sheets(ShtNm2).Cells(j11, i1 + 10).Value
Next i1
For i1 = 1 To 6 '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 6
Sheets(ShtNm2).Cells(n19, i2 + 20).Value = a5(i2 + (i1 - 1) * 6)
Next i2
Sheets(ShtNm2).Cells(n19, 9 + 20).Value = i1
Next i1
n20 = n20 - 6
120 Next j12
n20 = n20 - 6
110 Next j11
If n19 < 2 Then fl1 = 0
Return
' Construct Magic Set Diagonals
300 fl2 = 1
For i1 = 1 To 6
a2(i1) = Sheets(ShtNm2).Cells(j300, i1 + 10).Value
Next i1
For i1 = 1 To 6
a20 = a2(i1)
For i2 = 1 To n20
If a20 = a5(i2) Then fl2 = 0: Return
Next i2
Next i1
n20 = n20 + 6
i2 = 0
For i1 = n20 - 6 + 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 6
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 6
For i2 = 1 To 6
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 6 'rows
n21 = 0
For i2 = 1 To 6 'clmns
If a4(i1, i2) <> 0 Then
n21 = n21 + 1
If n21 = 1 Then i41 = i2 Else i42 = i2
End If
Next i2
For i3 = i1 + 1 To 6
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
Return
' Prepare Scratch Sheet
500
i9 = 0: n(1, 1) = 1
For i1 = 1 To 6
For i2 = 1 To 6
For i3 = 1 To 6
For i4 = 1 To 6
For i5 = 1 To 6
For i6 = 1 To 6
s11 = a0(1, i1) + a0(2, i2) + a0(3, i3) + a0(4, i4) + a0(5, i5) + a0(6, i6)
If s11 <> s1 Then GoTo 560
s12 = a0(1, i1) ^ 2 + a0(2, i2) ^ 2 + a0(3, i3) ^ 2 + a0(4, i4) ^ 2 + a0(5, i5) ^ 2 + a0(6, i6) ^ 2
If s12 <> s2 Then GoTo 560
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)
Cells(i9, 6).Value = a0(6, i6)
560 Next i6
550 Next i5
540 Next i4
530 Next i3
520 Next i2
n(i1, 2) = i9: If i1 <> 6 Then n(i1 + 1, 1) = i9 + 1
510 Next i1
n(6, 2) = i9
Return
' Print Semi Magic Squares
' Required Transformation Highlighted
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 = Nc9 ''n9
Cells(k1, k2 + 2).Value = n29
Cells(k1, k2 + 6).Value = j100 'Generator Bimagic Lines
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
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 + 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
Cells(k1, k2 + 2).Value = n29
Cells(k1, k2 + 6).Value = j100 'Generator Bimagic Lines
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
