Vorige Pagina About the Author

' Generates Prime Number Composed Magic Squares of order 13
' Completes Eccentric Square H9

' Tested with Office 2007 under Windows 7

Sub PriemH9()

    Dim a1(2448), a13(169), a(35), a9(81), b1(43300), b(43300), c(81)
 
    y = MsgBox("Locked", vbCritical, "Routine PriemH9")
    End

    Sheets("Klad1").Select

    n5 = 0: n9 = 0: k1 = 1: k2 = 1
    ShtNm1 = "Pairs7"
    ShtNm2 = "J2"
    
    t1 = Timer

    For j100 = 2 To 65

'       Start Reading Data ShtNm2
    
        Rcrd1a = Sheets(ShtNm2).Cells(j100, 171).Value
        MC13 = Sheets(ShtNm2).Cells(j100, 170).Value

'       Read Prime Numbers From Sheet ShtNm1

        Pr3 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value
        s1 = Sheets(ShtNm1).Cells(Rcrd1a, 5).Value       'MC3
        Cntr3 = Sheets(ShtNm1).Cells(Rcrd1a, 6).Value    'Center Element
        s9 = 9 * Cntr3                                   'MC9
        s13 = 13 * Cntr3                                 'MC13
        nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value

        If nVar < 169 Then GoTo 1000

        If MC13 <> s13 Then
                y = MsgBox("Conflict in Data", vbCritical, "Read " + ShtNm2)
                End
        End If

        Erase b1
        For j1 = 1 To nVar
            x = Sheets(ShtNm1).Cells(Rcrd1a, 9 + j1).Value
            b1(x) = x
        Next j1
        pMax = Sheets(ShtNm1).Cells(Rcrd1a, 9 + nVar).Value
    
'       Read Partly Completed Square 13 x 13
        
        For i1 = 1 To 169
            a13(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
        Next i1
        GoSub 950      'Remove used primes from available primes
       
        s92 = a13(33) + a13(47) + a13(61) + a13(75) + a13(89)
        
        a9(19) = a13(31):  a9(20) = a13(32):  a9(21) = a13(33):  a9(22) = a13(34):  a9(23) = a13(35):  a9(24) = a13(36):  a9(25) = a13(37):
        a9(28) = a13(44):  a9(29) = a13(45):  a9(30) = a13(46):  a9(31) = a13(47):  a9(32) = a13(48):  a9(33) = a13(49):  a9(34) = a13(50):
        a9(37) = a13(57):  a9(38) = a13(58):  a9(39) = a13(59):  a9(40) = a13(60):  a9(41) = a13(61):  a9(42) = a13(62):  a9(43) = a13(63):
        a9(46) = a13(70):  a9(47) = a13(71):  a9(48) = a13(72):  a9(49) = a13(73):  a9(50) = a13(74):  a9(51) = a13(75):  a9(52) = a13(76):
        a9(55) = a13(83):  a9(56) = a13(84):  a9(57) = a13(85):  a9(58) = a13(86):  a9(59) = a13(87):  a9(60) = a13(88):  a9(61) = a13(89):
        a9(64) = a13(96):  a9(65) = a13(97):  a9(66) = a13(98):  a9(67) = a13(99):  a9(68) = a13(100): a9(69) = a13(101): a9(70) = a13(102):
        a9(73) = a13(109): a9(74) = a13(110): a9(75) = a13(111): a9(76) = a13(112): a9(77) = a13(113): a9(78) = a13(114): a9(79) = a13(115):

'       Reassign Center
        
        b1(Cntr3) = Cntr3

'       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
        If a1(1) = 1 Then m1 = 2: m2 = m2 - 1

'       Determine Magic Square Order 3

t11 = Timer                                                     'Time Out

For j9 = m1 To m2                                                     'a(9)
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)

For j8 = m1 To m2                                                     'a(8)
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)

    a(7) = s1 - a(8) - a(9):
    If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70:
    If b1(a(7)) = 0 Then GoTo 70
    If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
    
    a(6) = 4 * s1 / 3 - a(8) - 2 * a(9):
    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

    a(5) = s1 / 3:
    If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50:
    If b1(a(5)) = 0 Then GoTo 50
    If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
    
    a(4) = -2 * s1 / 3 + a(8) + 2 * a(9):
    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
    
    a(3) = -s1 / 3 + a(8) + a(9):
    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(2) = 2 * s1 / 3 - a(8):
    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
    
    a(1) = 2 * s1 / 3 - a(9):
    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
                          
    a9(7) = a(8):   a9(8) = a(9):   a9(9) = a(7):
    a9(16) = a(2):  a9(17) = a(3):  a9(18) = a(1):
                    a9(26) = a(6):  a9(27) = a(4):

t12 = Timer: t13 = t12 - t11                                  'Time Out
If t13 > 60 Then Erase b1, b, c: GoTo 1000                    'Time Out, Try Next

                          GoSub 2000                          'Determine Main Diagonal and Remaining Pairs
                          If fl1 = 0 Then GoTo 5
                          
                          GoSub 800: If fl1 = 0 Then GoTo 5   'Back Check Identical Numbers a9()
                          n9 = n9 + 1: GoSub 650              'Print Results Squares a9()

'                         GoSub 655                           'Complete a13() with a9()
'                         GoSub 850: If fl1 = 0 Then GoTo 5   'Back Check Identical Numbers a13()
'                         n9 = n9 + 1: GoSub 660              'Print Results Squares a13()

                          Erase b1, b, c: GoTo 1000

                         
5  b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(2) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 Next j8
    
    b(c(9)) = 0: c(9) = 0
90 Next j9

     Erase b1, b, c
1000 Next j100

    t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
    y = MsgBox(t10, 0, "Routine PriemH9")

End

'   Determine Main Diagonal and Remaining Pairs

2000 fl1 = 1

'   Main Diagonal and Related Border Pairs

    For j10 = m1 To m2
    If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
    a(10) = a1(j10)
    
    a(14) = Pr3 - a(10): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
    
    For j11 = m1 To m2
    If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
    a(11) = a1(j11)
   
    a(15) = Pr3 - a(11): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
  
    For j12 = m1 To m2
    If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
    a(12) = a1(j12)
    
    a(16) = Pr3 - a(12): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
    
    a(13) = (s9 - s92) - a(12) - a(11) - a(10)
    If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130:
    If b1(a(13)) = 0 Then GoTo 130
    If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
    
    a(17) = Pr3 - a(13): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
    
    a(18) = s1 - a(13) - a(16)
    If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180:
    If b1(a(18)) = 0 Then GoTo 180
    If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
    
    a(20) = Pr3 - a(18): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
    
    a(19) = s1 - a(10) - a(15)
    If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190:
    If b1(a(19)) = 0 Then GoTo 190
    If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
    
    a(21) = Pr3 - a(19): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210

'   Remaining Border Pairs

    For j22 = m1 To m2
    If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
    a(22) = a1(j22)

    a(25) = Pr3 - a(22): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250

    For j23 = m1 To m2
    If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
    a(23) = a1(j23)

    a(26) = Pr3 - a(23): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260

    a(24) = s1 - a(22) - a(23)
    If a(24) < a1(m1) Or a(24) > a1(m2) Then GoTo 240:
    If b1(a(24)) = 0 Then GoTo 240
    If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240

    a(27) = Pr3 - a(24): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270

    For j28 = m1 To m2
    If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
    a(28) = a1(j28)

    a(31) = Pr3 - a(28): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310

    For j29 = m1 To m2
    If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
    a(29) = a1(j29)

    a(32) = Pr3 - a(29): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320

    a(30) = s1 - a(28) - a(29)
    If a(30) < a1(m1) Or a(30) > a1(m2) Then GoTo 300:
    If b1(a(30)) = 0 Then GoTo 300
    If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300

    a(33) = Pr3 - a(30): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330

    a9(1) = a(10):  a9(10) = a(14):
    a9(11) = a(11): a9(2) = a(15):
    a9(71) = a(12): a9(72) = a(16):
    a9(81) = a(13): a9(80) = a(17):
           
    a9(63) = a(18): a9(62) = a(20):
    a9(3) = a(19):  a9(12) = a(21):

    a9(4) = a(22):  a9(5) = a(23):  a9(6) = a(24):
    a9(13) = a(25): a9(14) = a(26): a9(15) = a(27):

    a9(35) = a(28): a9(44) = a(29): a9(53) = a(30):
    a9(36) = a(31): a9(45) = a(32): a9(54) = a(33):

    Return

    b(c(33)) = 0: c(33) = 0
330 b(c(30)) = 0: c(30) = 0
300 b(c(32)) = 0: c(32) = 0
320 b(c(29)) = 0: c(29) = 0
290 Next j29

    b(c(31)) = 0: c(31) = 0
310 b(c(28)) = 0: c(28) = 0
280 Next j28

    b(c(27)) = 0: c(27) = 0
270 b(c(24)) = 0: c(24) = 0
240 b(c(26)) = 0: c(26) = 0
260 b(c(23)) = 0: c(23) = 0
230 Next j23

    b(c(25)) = 0: c(25) = 0
250 b(c(22)) = 0: c(22) = 0
220 Next j22
    
    b(c(21)) = 0: c(21) = 0
210 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(18)) = 0: c(18) = 0
180 b(c(17)) = 0: c(17) = 0
170 b(c(13)) = 0: c(13) = 0
130 b(c(16)) = 0: c(16) = 0
160 b(c(12)) = 0: c(12) = 0
120 Next j12

    b(c(15)) = 0: c(15) = 0
150 b(c(11)) = 0: c(11) = 0
110 Next j11

    b(c(14)) = 0: c(14) = 0
140 b(c(10)) = 0: c(10) = 0
100 Next j10

    fl1 = 0
    
    Return

'   Print Results Squares a9()

650  n5 = n5 + 1
     If n5 = 3 Then
         n5 = 1: k1 = k1 + 10: k2 = 1
     Else
         If n9 > 1 Then k2 = k2 + 10
     End If
     
     Cells(k1, k2 + 1).Select
     Cells(k1, k2 + 1).Font.Color = -4165632
     Cells(k1, k2 + 1).Value = "MC = " + CStr(s9)

     i3 = 0
     For i1 = 1 To 9
         For i2 = 1 To 9
             i3 = i3 + 1
             Cells(k1 + i1, k2 + i2).Value = a9(i3)
         Next i2
     Next i1
    
     Return
     
'    Complete a13() with a9()
     
655
    a13(5) = a9(1):    a13(6) = a9(2):   a13(7) = a9(3):   a13(8) = a9(4):   a13(9) = a9(5):   a13(10) = a9(6):  a13(11) = a9(7):
    a13(12) = a9(8):   a13(13) = a9(9):
    a13(18) = a9(10):  a13(19) = a9(11): a13(20) = a9(12): a13(21) = a9(13): a13(22) = a9(14): a13(23) = a9(15): a13(24) = a9(16):
    a13(25) = a9(17):  a13(26) = a9(18):
    
    a13(38) = a9(26):  a13(39) = a9(27):
    a13(51) = a9(35):  a13(52) = a9(36):
    a13(64) = a9(44):  a13(65) = a9(45):
    a13(77) = a9(53):  a13(78) = a9(54):
    a13(90) = a9(62):  a13(91) = a9(63):
    a13(103) = a9(71): a13(104) = a9(72):
    a13(116) = a9(80): a13(117) = a9(81):
    
    Return
     
'   Print Results Squares a13()

660  n5 = n5 + 1
     If n5 = 2 Then
         n5 = 1: k1 = k1 + 14: k2 = 1
     Else
         If n9 > 1 Then k2 = k2 + 14
     End If
     
     Cells(k1, k2 + 1).Select
     Cells(k1, k2 + 1).Font.Color = -4165632
     Cells(k1, k2 + 1).Value = "MC = " + CStr(s13)

     i3 = 0
     For i1 = 1 To 13
         For i2 = 1 To 13
             i3 = i3 + 1
             Cells(k1 + i1, k2 + i2).Value = a13(i3)
         Next i2
     Next i1
    
     Return

'   Double Check Identical Numbers a9()

800 fl1 = 1
    For j1 = 1 To 81
       a20 = a9(j1): If a20 = 0 Then GoTo 810
       For j2 = (1 + j1) To 81
           If a20 = a9(j2) Then fl1 = 0: Return
       Next j2
810 Next j1
    Return
    
'   Double Check Identical Numbers a13()

850 fl1 = 1
    For j1 = 1 To 169
       a20 = a13(j1): If a20 = 0 Then GoTo 860
       For j2 = (1 + j1) To 169
           If a20 = a13(j2) Then fl1 = 0: Return
       Next j2
860 Next j1
    Return

'   Remove used pairs from b1()

950 For j1 = 1 To 169
        b1(a13(j1)) = 0
    Next j1
    Return

End Sub

Vorige Pagina About the Author