' Constructs 11 x 11 Bordered Magic Squares (Part 1)
' - Reads One Symmetric Magic Center Square Order 5
' - Generates Anti Symmetric Semi Magic Corner Squares (3 x 3) for Composed Border (11 x 11)
' Tested with Office 2007 under Windows 7
Sub Priem11d1()
Dim a1(121), a11(121), a(25), b1(121), b(121), c(25), a2(9), b2(121), c2(9)
y = MsgBox("Locked", vbCritical, "Routine Priem11d1")
End
n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0: n10 = 0
ShtNm2 = "Solutions5"
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
Pr3 = 122: Cntr3 = 61: nVar = 121
s1 = 3 * Cntr3 'MC3
s5 = 5 * Cntr3 'MC5
s11 = 11 * Cntr3 'MC11
For j100 = 244 To 1065
' Redefine Integers
Erase b1
For i1 = 1 To nVar
b1(i1) = i1
Next i1
pMax = 121
' Read Symmetric Magic Square (5 x 5)
For i1 = 1 To 25
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n31 = 1: n32 = 25: GoSub 900 'Remove used integers from available integers
Erase a11
' Store in a11()
a11(37) = a(1): a11(38) = a(2): a11(39) = a(3): a11(40) = a(4): a11(41) = a(5):
a11(48) = a(6): a11(49) = a(7): a11(50) = a(8): a11(51) = a(9): a11(52) = a(10):
a11(59) = a(11): a11(60) = a(12): a11(61) = a(13): a11(62) = a(14): a11(63) = a(15):
a11(70) = a(16): a11(71) = a(17): a11(72) = a(18): a11(73) = a(19): a11(74) = a(20):
a11(81) = a(21): a11(82) = a(22): a11(83) = a(23): a11(84) = a(24): a11(85) = a(25):
Erase a
' Restore available pairs in a1()
n10 = 0
For j1 = 1 To pMax
If b1(j1) <> 0 Then
n10 = n10 + 1
a1(n10) = b1(j1)
End If
Next j1
m1 = 1: m2 = n10: n10 = 0
GoSub 2000 'Determine 4 Corner Squares
n10 = 0
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem11d1")
End
' Determine 4 Corner Squares
2000 Erase b2, c2
For jj9 = m1 To m2 'a2(9)
If b1(a1(jj9)) = 0 Then GoTo 165
If b2(a1(jj9)) = 0 Then b2(a1(jj9)) = a1(jj9): c2(9) = a1(jj9) Else GoTo 165
a2(9) = a1(jj9)
For jj8 = m1 To m2 'a2(8)
If b1(a1(jj8)) = 0 Then GoTo 125
If b2(a1(jj8)) = 0 Then b2(a1(jj8)) = a1(jj8): c2(8) = a1(jj8) Else GoTo 125
a2(8) = a1(jj8)
a2(7) = s1 - a2(8) - a2(9):
If a2(7) < a1(m1) Or a2(7) > a1(m2) Then GoTo 115:
If b1(a2(7)) = 0 Then GoTo 115
For jj6 = m1 To m2 'a2(6)
If b1(a1(jj6)) = 0 Then GoTo 100
If b2(a1(jj6)) = 0 Then b2(a1(jj6)) = a1(jj6): c2(6) = a1(jj6) Else GoTo 100
a2(6) = a1(jj6)
a2(5) = -s1 + a2(6) + a2(8) + 2 * a2(9)
If a2(5) < a1(m1) Or a2(5) > a1(m2) Then GoTo 80:
If b1(a2(5)) = 0 Then GoTo 80
a2(4) = 2 * s1 - 2 * a2(6) - a2(8) - 2 * a2(9)
If a2(4) < a1(m1) Or a2(4) > a1(m2) Then GoTo 80:
If b1(a2(4)) = 0 Then GoTo 80
a2(3) = s1 - a2(6) - a2(9)
If a2(3) < a1(m1) Or a2(3) > a1(m2) Then GoTo 80:
If b1(a2(3)) = 0 Then GoTo 80
a2(2) = 2 * s1 - a2(6) - 2 * a2(8) - 2 * a2(9)
If a2(2) < a1(m1) Or a2(2) > a1(m2) Then GoTo 80:
If b1(a2(2)) = 0 Then GoTo 80
a2(1) = -2 * s1 + 2 * a2(6) + 2 * a2(8) + 3 * a2(9)
If a2(1) < a1(m1) Or a2(1) > a1(m2) Then GoTo 80:
If b1(a2(1)) = 0 Then GoTo 80
' Exclude solutions with identical numbers a2()
GoSub 810: If fl1 = 0 Then GoTo 80
GoSub 1900: If fl1 = 0 Then GoTo 80 'Anti Symmetric
n10 = n10 + 1
If n10 < 2 Then
GoSub 750 'Transform and Assign Corner Squares
GoSub 910 'Remove used integers a2() from available integers b1()
Erase b2, c2: GoTo 165
Else
GoSub 750 'Transform and Assign Corner Squares
GoSub 850 'Double Check Identical Integers
If fl1 = 1 Then
' n9 = n9 + 1: GoSub 650 'Print Composed Squares
n9 = n9 + 1: GoSub 640 'Print Composed lines
End If
End If
If n10 = 2 Then Erase b2, c2: Return 'Only four squares required
80 b2(c2(6)) = 0: c2(6) = 0
100 Next jj6
115 b2(c2(8)) = 0: c2(8) = 0
125 Next jj8
b2(c2(9)) = 0: c2(9) = 0
165 Next jj9
Return
' Print results (lines)
640 Cells(n9, 123).Select
For i1 = 1 To 121
Cells(n9, i1).Value = a11(i1)
Next i1
Cells(n9, 122).Value = s11
Cells(n9, 123).Value = j100
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 2 Then
n2 = 1: k1 = k1 + 12: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 12
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s11)
i3 = 0
For i1 = 1 To 11
For i2 = 1 To 11
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a11(i3)
Next i2
Next i1
Return
' Transform and Assign Corner and Border Squares
750 Select Case n10
Case 1: 'Left Top
a11(1) = a2(3): a11(2) = a2(2): a11(3) = a2(1):
a11(12) = a2(6): a11(13) = a2(5): a11(14) = a2(4):
a11(23) = a2(9): a11(24) = a2(8): a11(25) = a2(7):
'Right Bottom
a11(97) = Pr3 - a11(25): a11(98) = Pr3 - a11(24): a11(99) = Pr3 - a11(23):
a11(108) = Pr3 - a11(14): a11(109) = Pr3 - a11(13): a11(110) = Pr3 - a11(12):
a11(119) = Pr3 - a11(3): a11(120) = Pr3 - a11(2): a11(121) = Pr3 - a11(1):
Case 2: 'Right Top
a11(9) = a2(1): a11(10) = a2(2): a11(11) = a2(3):
a11(20) = a2(4): a11(21) = a2(5): a11(22) = a2(6):
a11(31) = a2(7): a11(32) = a2(8): a11(33) = a2(9):
'Left Bottom
a11(89) = Pr3 - a11(33): a11(90) = Pr3 - a11(32): a11(91) = Pr3 - a11(31):
a11(100) = Pr3 - a11(22): a11(101) = Pr3 - a11(21): a11(102) = Pr3 - a11(20):
a11(111) = Pr3 - a11(11): a11(112) = Pr3 - a11(10): a11(113) = Pr3 - a11(9):
End Select
Return
' Exclude solutions with identical numbers a2()
810 fl1 = 1
For j1 = 1 To 9
a20 = a2(j1)
For j2 = (1 + j1) To 9
If a20 = a2(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Exclude solutions with identical numbers a11()
850 fl1 = 1
For j1 = 1 To 121
a20 = a11(j1): If a20 = 0 Then GoTo 855
For j2 = (1 + j1) To 121
If a20 = a11(j2) Then fl1 = 0: Return
Next j2
855 Next j1
Return
' Remove used integers a() from available integers b1()
900 For i1 = n31 To n32
b1(a(i1)) = 0
Next i1
Return
' Remove used integers a2() and complements from available integers b1()
910 For i1 = 1 To 9
b1(a2(i1)) = 0: b1(Pr3 - a2(i1)) = 0
Next i1
Return
' Check Pairs
1900 fl1 = 1: n25 = 0
For j1 = 1 To 9
a20 = Pr3 - a2(j1) 'Complement
For j2 = (1 + j1) To 9
If a20 = a2(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
