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' Generates Concentric Magic Squares of order 9 with 4 x 3 Even Corner Numbers
' Suitable for Concentric Lozenge Squares of order 13 (Predefined Border)

' Tested with Office 2007 under Windows 7

Sub Priem9c1()

Dim a1(121), a(81), a7(49), b(167), b1(167), c(81)

y = MsgBox("Locked", vbCritical, "Routine Priem9c")
End

    n5 = 0: n9 = 0: k1 = 1: k2 = 1

    Sheets("Klad1").Select
    
    t1 = Timer

For j100 = 2 To 49 ''365

'   Define Variables

    a1(1) = 3:     a1(2) = 4:     a1(3) = 5:     a1(4) = 6:     a1(5) = 7:
    a1(6) = 8:     a1(7) = 9:     a1(8) = 10:    a1(9) = 11:
    a1(10) = 15:   a1(11) = 17:   a1(12) = 18:   a1(13) = 19:   a1(14) = 20:
    a1(15) = 21:   a1(16) = 22:   a1(17) = 23:   a1(18) = 25:
    a1(19) = 27:   a1(20) = 29:   a1(21) = 31:   a1(22) = 32:   a1(23) = 33:
    a1(24) = 34:   a1(25) = 35:   a1(26) = 37:   a1(27) = 39:
    a1(28) = 40:   a1(29) = 41:   a1(30) = 43:   a1(31) = 45:   a1(32) = 46:
    a1(33) = 47:   a1(34) = 49:   a1(35) = 51:   a1(36) = 52:
    a1(37) = 53:   a1(38) = 54:   a1(39) = 55:   a1(40) = 57:   a1(41) = 59:
    a1(42) = 61:   a1(43) = 63:   a1(44) = 64:   a1(45) = 65:
    a1(46) = 66:   a1(47) = 67:   a1(48) = 68:   a1(49) = 69:   a1(50) = 71:
    a1(51) = 73:   a1(52) = 75:   a1(53) = 76:   a1(54) = 77:
    a1(55) = 78:   a1(56) = 79:   a1(57) = 80:   a1(58) = 81:   a1(59) = 82:
    a1(60) = 83:   a1(61) = 85:   a1(62) = 87:   a1(63) = 88:
    a1(64) = 89:   a1(65) = 90:   a1(66) = 91:   a1(67) = 92:   a1(68) = 93:
    a1(69) = 94:   a1(70) = 95:   a1(71) = 97:   a1(72) = 99:
    a1(73) = 101:  a1(74) = 102:  a1(75) = 103:  a1(76) = 104:  a1(77) = 105:
    a1(78) = 106:  a1(79) = 107:  a1(80) = 109:  a1(81) = 111:
    a1(82) = 113:  a1(83) = 115:  a1(84) = 116:  a1(85) = 117:  a1(86) = 118:
    a1(87) = 119:  a1(88) = 121:  a1(89) = 123:  a1(90) = 124:
    a1(91) = 125:  a1(92) = 127:  a1(93) = 129:  a1(94) = 130:  a1(95) = 131:
    a1(96) = 133:  a1(97) = 135:  a1(98) = 136:  a1(99) = 137:
    a1(100) = 138: a1(101) = 139: a1(102) = 141: a1(103) = 143: a1(104) = 145:
    a1(105) = 147: a1(106) = 148: a1(107) = 149: a1(108) = 150:
    a1(109) = 151: a1(110) = 152: a1(111) = 153: a1(112) = 155: a1(113) = 159:
    a1(114) = 160: a1(115) = 161: a1(116) = 162: a1(117) = 163:
    a1(118) = 164: a1(119) = 165: a1(120) = 166: a1(121) = 167:
    
    s1 = 765: p2 = 170: m1 = 1: m2 = 121
    aMin = a1(1): aMax = a1(121)

    Erase b1
    For i1 = m1 To m2
        b1(a1(i1)) = a1(i1)
    Next i1

'   Read Center Square

    For i1 = 1 To 49
        a7(i1) = Sheets("Center7").Cells(j100, i1):  b1(a7(i1)) = 0
    Next i1
    
'   Reduce Variables

    i2 = 0
    For i1 = aMin To aMax
        If b1(i1) = i1 Then
           i2 = i2 + 1: a1(i2) = i1
        End If
    Next i1
    m2 = i2

    Erase b1
    For i1 = m1 To m2
        b1(a1(i1)) = a1(i1)
    Next i1
    
'   Store Center Square in a()
    
    Erase a
    a(11) = a7(1):  a(12) = a7(2):  a(13) = a7(3):  a(14) = a7(4):  a(15) = a7(5):  a(16) = a7(6):  a(17) = a7(7):
    a(20) = a7(8):  a(21) = a7(9):  a(22) = a7(10): a(23) = a7(11): a(24) = a7(12): a(25) = a7(13): a(26) = a7(14):
    a(29) = a7(15): a(30) = a7(16): a(31) = a7(17): a(32) = a7(18): a(33) = a7(19): a(34) = a7(20): a(35) = a7(21):
    a(38) = a7(22): a(39) = a7(23): a(40) = a7(24): a(41) = a7(25): a(42) = a7(26): a(43) = a7(27): a(44) = a7(28):
    a(47) = a7(29): a(48) = a7(30): a(49) = a7(31): a(50) = a7(32): a(51) = a7(33): a(52) = a7(34): a(53) = a7(35):
    a(56) = a7(36): a(57) = a7(37): a(58) = a7(38): a(59) = a7(39): a(60) = a7(40): a(61) = a7(41): a(62) = a7(42):
    a(65) = a7(43): a(66) = a7(44): a(67) = a7(45): a(68) = a7(46): a(69) = a7(47): a(70) = a7(48): a(71) = a7(49):

'   Determine Border(s)

    For j81 = m1 To m2                                                    'a(81) even
    If CInt(a1(j81) / 2) <> a1(j81) / 2 Then GoTo 810
    If b(a1(j81)) = 0 Then b(a1(j81)) = a1(j81): c(81) = a1(j81) Else GoTo 810
    a(81) = a1(j81)
   
    a(1) = p2 - a(81): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
    
    For j80 = m1 To m2                                                    'a(80) even
    If CInt(a1(j80) / 2) <> a1(j80) / 2 Then GoTo 800
    If b(a1(j80)) = 0 Then b(a1(j80)) = a1(j80): c(80) = a1(j80) Else GoTo 800
    a(80) = a1(j80)
   
    a(8) = p2 - a(80): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
    
    For j79 = m1 To m2                                                    'a(79)odd
    If CInt(a1(j79) / 2) = a1(j79) / 2 Then GoTo 790
    If b(a1(j79)) = 0 Then b(a1(j79)) = a1(j79): c(79) = a1(j79) Else GoTo 790
    a(79) = a1(j79)
   
    a(7) = p2 - a(79): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
    
    For j78 = m1 To m2                                                    'a(78)odd
    If CInt(a1(j78) / 2) = a1(j78) / 2 Then GoTo 780
    If b(a1(j78)) = 0 Then b(a1(j78)) = a1(j78): c(78) = a1(j78) Else GoTo 780
    a(78) = a1(j78)
   
    a(6) = p2 - a(78): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
    
    For j77 = m1 To m2                                                    'a(77) odd
    If CInt(a1(j77) / 2) = a1(j77) / 2 Then GoTo 770
    If b(a1(j77)) = 0 Then b(a1(j77)) = a1(j77): c(77) = a1(j77) Else GoTo 770
    a(77) = a1(j77)
    
    a(5) = p2 - a(77): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
    
    For j76 = m1 To m2                                                    'a(76) odd
    If CInt(a1(j76) / 2) = a1(j76) / 2 Then GoTo 760
    If b(a1(j76)) = 0 Then b(a1(j76)) = a1(j76): c(76) = a1(j76) Else GoTo 760
    a(76) = a1(j76)
    
    a(4) = p2 - a(76): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
    
    For j75 = m1 To m2                                                    'a(75) odd
    If CInt(a1(j75) / 2) = a1(j75) / 2 Then GoTo 750
    If b(a1(j75)) = 0 Then b(a1(j75)) = a1(j75): c(75) = a1(j75) Else GoTo 750
    a(75) = a1(j75)
   
    a(3) = p2 - a(75): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
    
    For j74 = m1 To m2                                                    'a(74) even
    If CInt(a1(j74) / 2) <> a1(j74) / 2 Then GoTo 740
    If b(a1(j74)) = 0 Then b(a1(j74)) = a1(j74): c(74) = a1(j74) Else GoTo 740
    a(74) = a1(j74)
   
    a(73) = s1 - a(74) - a(75) - a(76) - a(77) - a(78) - a(79) - a(80) - a(81)
    If CInt(a(73) / 2) <> a(73) / 2 Then GoTo 730                         'a(73) even
    If a(73) < a1(m1) Or a(73) > a1(m2) Then GoTo 730
    If b1(a(73)) = 0 Then GoTo 730
    If b(a(73)) = 0 Then b(a(73)) = a(73): c(73) = a(73) Else GoTo 730
    
    a(9) = p2 - a(73): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
    a(2) = p2 - a(74): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
    
    For j72 = m1 To m2                                                    'a(72) even
    If CInt(a1(j72) / 2) <> a1(j72) / 2 Then GoTo 720
    If b(a1(j72)) = 0 Then b(a1(j72)) = a1(j72): c(72) = a1(j72) Else GoTo 720
    a(72) = a1(j72)
    
    a(64) = p2 - a(72): If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640
    
    For j63 = m1 To m2                                                    'a(63) odd
    If CInt(a1(j63) / 2) = a1(j63) / 2 Then GoTo 630
    If b(a1(j63)) = 0 Then b(a1(j63)) = a1(j63): c(63) = a1(j63) Else GoTo 630
    a(63) = a1(j63)
    
    a(55) = p2 - a(63): If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
    
    For j54 = m1 To m2                                                    'a(54) odd
    If CInt(a1(j54) / 2) = a1(j54) / 2 Then GoTo 540
    If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
    a(54) = a1(j54)
    
    a(46) = p2 - a(54): If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
    
    For j45 = m1 To m2                                                     'a(45) odd
    If CInt(a1(j45) / 2) = a1(j45) / 2 Then GoTo 450
    If b(a1(j45)) = 0 Then b(a1(j45)) = a1(j45): c(45) = a1(j45) Else GoTo 450
    a(45) = a1(j45)
    
    a(37) = p2 - a(45): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370

    For j36 = m1 To m2                                                     'a(36) odd
    If CInt(a1(j36) / 2) = a1(j36) / 2 Then GoTo 360
    If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
    a(36) = a1(j36)
    
    a(28) = p2 - a(36): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
    
    For j27 = m1 To m2                                                    'a(27) odd
    If CInt(a1(j27) / 2) = a1(j27) / 2 Then GoTo 270
    If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
    a(27) = a1(j27)
    
    a(19) = p2 - a(27): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
    
    a(18) = 7 * p2 / 2 - a(27) - a(36) - a(45) - a(54) - a(63) - a(72) + a(73) - a(81)
    If CInt(a(18) / 2) <> a(18) / 2 Then GoTo 180                          'a(18) even
    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(10) = p2 - a(18): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
    
'                               Exclude solutions with identical numbers

                                GoSub 1800: If fl1 = 0 Then GoTo 5
    
                                n9 = n9 + 1
                                GoSub 2650              'Print results (squares)
 '                              GoSub 2645              'Print results (selected numbers)

                                Erase b, c: GoTo 1000   'Print only first square

5
        b(c(10)) = 0: c(10) = 0
100     b(c(18)) = 0: c(18) = 0
180     b(c(19)) = 0: c(19) = 0
190     b(c(27)) = 0: c(27) = 0
270     Next j27
        
        b(c(28)) = 0: c(28) = 0
280     b(c(36)) = 0: c(36) = 0
360     Next j36
        
        b(c(37)) = 0: c(37) = 0
370     b(c(45)) = 0: c(45) = 0
450     Next j45
        
        b(c(46)) = 0: c(46) = 0
460     b(c(54)) = 0: c(54) = 0
540     Next j54
        
        b(c(55)) = 0: c(55) = 0
550     b(c(63)) = 0: c(63) = 0
630     Next j63
        
        b(c(64)) = 0: c(64) = 0
640     b(c(72)) = 0: c(72) = 0
720     Next j72
    
        b(c(2)) = 0: c(2) = 0
20      b(c(9)) = 0: c(9) = 0
90      b(c(73)) = 0: c(73) = 0
730     b(c(74)) = 0: c(74) = 0
740     Next j74
        b(c(3)) = 0: c(3) = 0
30      b(c(75)) = 0: c(75) = 0
750     Next j75
        b(c(4)) = 0: c(4) = 0
40      b(c(76)) = 0: c(76) = 0
760     Next j76
        b(c(5)) = 0: c(5) = 0
50      b(c(77)) = 0: c(77) = 0
770     Next j77
        b(c(6)) = 0: c(6) = 0
60      b(c(78)) = 0: c(78) = 0
780     Next j78
        b(c(7)) = 0: c(7) = 0
70      b(c(79)) = 0: c(79) = 0
790     Next j79
        b(c(8)) = 0: c(8) = 0
80      b(c(80)) = 0: c(80) = 0
800     Next j80
        b(c(1)) = 0: c(1) = 0
10      b(c(81)) = 0: c(81) = 0
810     Next j81
    
     Erase b, c
1000 Next j100

    t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
    y = MsgBox(t10, 0, "Routine Priem9c")

End
     
'   Print results (selected numbers)

2645 For i1 = 1 To 81
         Cells(n9, i1).Value = a(i1)
     Next i1
     Cells(n9, 82).Value = n9
     Cells(n9, 82).Select
     Return

'   Print results (squares)

2650 n5 = n5 + 1
     If n5 = 4 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 = n9
    
     i3 = 0
     For i1 = 1 To 9
         For i2 = 1 To 9
             i3 = i3 + 1
             Cells(k1 + i1, k2 + i2).Value = a(i3)
         Next i2
     Next i1
    
     Return
     
'   Exclude solutions with identical numbers

1800 fl1 = 1
     For j1 = 1 To 81
        a2 = a(j1): If a2 = 0 Then GoTo 1810
        For j2 = (1 + j1) To 81
            If a2 = a(j2) Then fl1 = 0: Return
        Next j2
1810 Next j1
     Return
     
End Sub

Vorige Pagina About the Author