Vorige Pagina About the Author

' Generates Prime Number Simple Magic Cubes of order 4
' Pantriagonal and Complete (Frost)

' Tested with Office 2007 under Windows 7

Sub PrimeCubes46()

Dim a1(724), a(64), b1(43291), b(43291), c(64)

y = MsgBox("Locked", vbCritical, "Routine PrimeCubes46")
End

    n2 = 0: n9 = 0: k1 = 1: k2 = 1

'   Generate data
    
    Sheets("Klad1").Select
    
    t1 = Timer

For j100 = 1 To 96 

'   Define variables

''  GoSub 2000           ' Read Natural Numbers                    (j100 = 1 To 1)
''  GoSub 2010           ' Read Prime Numbers From sheet "Pairs8"  (j100:  As selected)
    GoSub 2020           ' Read Prime Numbers from sheet "Lines72" (j100 = 1 To 96)

    For j64 = m1 To m2                                                       'a(64)
    If b(a1(j64)) = 0 Then b(a1(j64)) = a1(j64): c(64) = a1(j64) Else GoTo 640
    a(64) = a1(j64)

    a(22) = s1 / 2 - a(64): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220

    For j63 = m1 To m2                                                      'a(63)
    If b(a1(j63)) = 0 Then b(a1(j63)) = a1(j63): c(63) = a1(j63) Else GoTo 630
    a(63) = a1(j63)
    
    a(21) = s1 / 2 - a(63): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
    
    For j62 = m1 To m2                                                      'a(62)
    If b(a1(j62)) = 0 Then b(a1(j62)) = a1(j62): c(62) = a1(j62) Else GoTo 620
    a(62) = a1(j62)
    
    a(61) = s1 - a(62) - a(63) - a(64): If a(61) < a1(m1) Or a(61) > a1(m2) Then GoTo 610
    If b1(a(61)) = 0 Then GoTo 610
    If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610

    a(24) = s1 / 2 - a(62): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
    a(23) = s1 / 2 - a(61): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230

    For j60 = m1 To m2                                                      'a(60)
    If b(a1(j60)) = 0 Then b(a1(j60)) = a1(j60): c(60) = a1(j60) Else GoTo 600
    a(60) = a1(j60)

    a(18) = s1 / 2 - a(60): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180

    For j59 = m1 To m2                                                        'a(59)
    If b(a1(j59)) = 0 Then b(a1(j59)) = a1(j59): c(59) = a1(j59) Else GoTo 590
    a(59) = a1(j59)

    a(17) = s1 / 2 - a(59): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
    
    For j58 = m1 To m2                                                      'a(58)
    If b(a1(j58)) = 0 Then b(a1(j58)) = a1(j58): c(58) = a1(j58) Else GoTo 580
    a(58) = a1(j58)

    a(57) = s1 - a(58) - a(59) - a(60): If a(57) < a1(m1) Or a(57) > a1(m2) Then GoTo 570
    If b1(a(57)) = 0 Then GoTo 570
    If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570

    a(20) = s1 / 2 - a(58): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
    a(19) = s1 / 2 - a(57): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
    
    For j56 = m1 To m2                                                      'a(56)
    If b(a1(j56)) = 0 Then b(a1(j56)) = a1(j56): c(56) = a1(j56) Else GoTo 560
    a(56) = a1(j56)
    
    a(52) = s1 - a(56) - a(60) - a(64): If a(52) < a1(m1) Or a(52) > a1(m2) Then GoTo 520
    If b1(a(52)) = 0 Then GoTo 520
    If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
    
    a(30) = s1 / 2 - a(56): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
    a(26) = s1 / 2 - a(52): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
    
    For j55 = m1 To m2                                                      'a(55)
    If b(a1(j55)) = 0 Then b(a1(j55)) = a1(j55): c(55) = a1(j55) Else GoTo 550
    a(55) = a1(j55)
    
    a(51) = s1 - a(55) - a(59) - a(63): If a(51) < a1(m1) Or a(51) > a1(m2) Then GoTo 510
    If b1(a(51)) = 0 Then GoTo 510
    If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
    
    a(29) = s1 / 2 - a(55): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
    a(25) = s1 / 2 - a(51): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250

    For j54 = m1 To m2                                                      'a(54)
    If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
    a(54) = a1(j54)

    a(53) = s1 - a(54) - a(55) - a(56): If a(53) < a1(m1) Or a(53) > a1(m2) Then GoTo 530
    If b1(a(53)) = 0 Then GoTo 530
    If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530

    a(50) = s1 - a(54) - a(58) - a(62): If a(50) < a1(m1) Or a(50) > a1(m2) Then GoTo 500
    If b1(a(50)) = 0 Then GoTo 500
    If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
    
    a(49) = s1 - a(53) - a(57) - a(61): If a(49) < a1(m1) Or a(49) > a1(m2) Then GoTo 490
    If b1(a(49)) = 0 Then GoTo 490
    If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
    
    a(32) = s1 / 2 - a(54): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
    a(31) = s1 / 2 - a(53): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
    a(28) = s1 / 2 - a(50): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
    a(27) = s1 / 2 - a(49): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270

    For j48 = m1 To m2                                                      'a(48)
    If b(a1(j48)) = 0 Then b(a1(j48)) = a1(j48): c(48) = a1(j48) Else GoTo 480
    a(48) = a1(j48)
    
    a(38) = a(48) - a(54) + a(64): If a(38) < a1(m1) Or a(38) > a1(m2) Then GoTo 380
    If b1(a(38)) = 0 Then GoTo 380
    If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
    
    a(16) = s1 / 2 - a(38): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
    a(6) = s1 / 2 - a(48): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60

    For j47 = m1 To m2                                                      'a(47)
    If b(a1(j47)) = 0 Then b(a1(j47)) = a1(j47): c(47) = a1(j47) Else GoTo 470
    a(47) = a1(j47)

    a(37) = a(47) - a(53) + a(63): If a(37) < a1(m1) Or a(37) > a1(m2) Then GoTo 370
    If b1(a(37)) = 0 Then GoTo 370
    If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
    
    a(15) = s1 / 2 - a(37): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
    a(5) = s1 / 2 - a(47): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
    
    For j46 = m1 To m2                                                      'a(46)
    If b(a1(j46)) = 0 Then b(a1(j46)) = a1(j46): c(46) = a1(j46) Else GoTo 460
    a(46) = a1(j46)
    
    a(45) = s1 - a(46) - a(47) - a(48): If a(45) < a1(m1) Or a(45) > a1(m2) Then GoTo 450
    If b1(a(45)) = 0 Then GoTo 450
    If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
    
    a(40) = a(46) - a(56) + a(62): If a(40) < a1(m1) Or a(40) > a1(m2) Then GoTo 400
    If b1(a(40)) = 0 Then GoTo 400
    If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
    
    a(39) = a(45) - a(55) + a(61): If a(39) < a1(m1) Or a(39) > a1(m2) Then GoTo 390
    If b1(a(39)) = 0 Then GoTo 390
    If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
    
    a(14) = s1 / 2 - a(40): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
    a(13) = s1 / 2 - a(39): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
    a(8) = s1 / 2 - a(46): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
    a(7) = s1 / 2 - a(45): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
    
    For j44 = m1 To m2                                                      'a(44)
    If b(a1(j44)) = 0 Then b(a1(j44)) = a1(j44): c(44) = a1(j44) Else GoTo 440
    a(44) = a1(j44)
    
    a(42) = 2 * s1 - a(44) - a(46) - a(48) - a(58) - a(60) - a(62) - a(64)
    If a(42) < a1(m1) Or a(42) > a1(m2) Then GoTo 420
    If b1(a(42)) = 0 Then GoTo 420
    If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
    
    a(36) = s1 - a(44) - a(46) - a(48) + a(56) - a(62):
    If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 360
    If b1(a(36)) = 0 Then GoTo 360
    If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
    
    a(34) = -s1 + a(44) + a(54) + a(58) + a(60) + a(62):
    If a(34) < a1(m1) Or a(34) > a1(m2) Then GoTo 340
    If b1(a(34)) = 0 Then GoTo 340
    If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
    
    a(12) = s1 / 2 - a(34): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
    a(10) = s1 / 2 - a(36): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
    a(4) = s1 / 2 - a(42): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
    a(2) = s1 / 2 - a(44): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20

    For j43 = m1 To m2                                                      'a(43)
    If b(a1(j43)) = 0 Then b(a1(j43)) = a1(j43): c(43) = a1(j43) Else GoTo 430
    a(43) = a1(j43)
    
    a(41) = s1 - a(42) - a(43) - a(44): If a(41) < a1(m1) Or a(41) > a1(m2) Then GoTo 410
    If b1(a(41)) = 0 Then GoTo 410
    If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
    
    a(35) = -a(43) + a(46) + a(48) + a(55) - a(61):
    If a(35) < a1(m1) Or a(35) > a1(m2) Then GoTo 350
    If b1(a(35)) = 0 Then GoTo 350
    If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
    
    a(33) = a(43) + a(53) - a(58) - a(60) + a(61):
    If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
    If b1(a(33)) = 0 Then GoTo 330
    If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
    
    a(11) = s1 / 2 - a(33): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
    a(9) = s1 / 2 - a(35): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
    a(3) = s1 / 2 - a(41): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
    a(1) = s1 / 2 - a(43): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
       

'           n9 = n9 + 1: GoSub 740 'Print results (selected numbers)
            n9 = n9 + 1: GoSub 750 'Print results (planes 1, 2, 3, 4)
            Erase b, c: GoTo 1000  'Print only first cube
    

    b(c(1)) = 0: c(1) = 0
10  b(c(3)) = 0: c(3) = 0
30  b(c(9)) = 0: c(9) = 0
90  b(c(11)) = 0: c(11) = 0
110 b(c(33)) = 0: c(33) = 0
330 b(c(35)) = 0: c(35) = 0
350 b(c(41)) = 0: c(41) = 0
410 b(c(43)) = 0: c(43) = 0
430 Next j43
    
    b(c(2)) = 0: c(2) = 0
20  b(c(4)) = 0: c(4) = 0
40  b(c(10)) = 0: c(10) = 0
100 b(c(12)) = 0: c(12) = 0
120 b(c(34)) = 0: c(34) = 0
340 b(c(36)) = 0: c(36) = 0
360 b(c(42)) = 0: c(42) = 0
420 b(c(44)) = 0: c(44) = 0
440 Next j44

    b(c(7)) = 0: c(7) = 0
70  b(c(8)) = 0: c(8) = 0
80  b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(39)) = 0: c(39) = 0
390 b(c(40)) = 0: c(40) = 0
400 b(c(45)) = 0: c(45) = 0
450 b(c(46)) = 0: c(46) = 0
460 Next j46

    b(c(5)) = 0: c(5) = 0
50  b(c(15)) = 0: c(15) = 0
150 b(c(37)) = 0: c(37) = 0
370 b(c(47)) = 0: c(47) = 0
470 Next j47
    
    b(c(6)) = 0: c(6) = 0
60  b(c(16)) = 0: c(16) = 0
160 b(c(38)) = 0: c(38) = 0
380 b(c(48)) = 0: c(48) = 0
480 Next j48

    b(c(27)) = 0: c(27) = 0
270 b(c(28)) = 0: c(28) = 0
280 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 b(c(49)) = 0: c(49) = 0
490 b(c(50)) = 0: c(50) = 0
500 b(c(53)) = 0: c(53) = 0
530 b(c(54)) = 0: c(54) = 0
540 Next j54

    b(c(25)) = 0: c(25) = 0
250 b(c(29)) = 0: c(29) = 0
290 b(c(51)) = 0: c(51) = 0
510 b(c(55)) = 0: c(55) = 0
550 Next j55

    b(c(26)) = 0: c(26) = 0
260 b(c(30)) = 0: c(30) = 0
300 b(c(52)) = 0: c(52) = 0
520 b(c(56)) = 0: c(56) = 0
560 Next j56

    b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(57)) = 0: c(57) = 0
570 b(c(58)) = 0: c(58) = 0
580 Next j58

    b(c(17)) = 0: c(17) = 0
170 b(c(59)) = 0: c(59) = 0
590 Next j59

    b(c(18)) = 0: c(18) = 0
180 b(c(60)) = 0: c(60) = 0
600 Next j60

    b(c(23)) = 0: c(23) = 0
230 b(c(24)) = 0: c(24) = 0
240 b(c(61)) = 0: c(61) = 0
610 b(c(62)) = 0: c(62) = 0
620 Next j62

    b(c(21)) = 0: c(21) = 0
210 b(c(63)) = 0: c(63) = 0
630 Next j63

    b(c(22)) = 0: c(22) = 0
220 b(c(64)) = 0: c(64) = 0
640 Next j64

1000 Next j100

    t2 = Timer
    
    t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
    y = MsgBox(t10, 0, "Routine PrimeCubes46")

End

'   Print results (selected numbers)

740 For i1 = 1 To 64
        Cells(n9, i1).Value = a(i1)
    Next i1
    
    Return

'   Print results (planes 11, 12, 13 and 14)

750 n2 = n2 + 1
    If n2 = 7 Then
        n2 = 1: k1 = k1 + 20: k2 = 1
    Else
        If n9 > 1 Then k2 = k2 + 5
    End If

    Cells(k1, k2 + 1).Select
    Cells(k1, k2 + 1).Font.Color = -4165632
    Cells(k1, k2 + 1).Value = "MC = " + CStr(s1)
       
    For i0 = 1 To 4
        i3 = (4 - i0) * 16
        For i1 = 1 To 4
            For i2 = 1 To 4
                i3 = i3 + 1
                Cells(k1 + i1 + (i0 - 1) * 5, k2 + i2).Value = a(i3)
            Next i2
        Next i1        
    Next i0
    
    Return

'    Read Natural Numbers

2000 For i1 = 1 To 64
         a1(i1) = i1
     Next i1
     m1 = 1: m2 = 64: s1 = 130

     Erase b1
     For i1 = m1 To m2
         b1(a1(i1)) = a1(i1)
     Next i1
     Return
     
'    Read Prime Numbers From sheet "Pairs8"

2010 s1 = 2 * Sheets("Pairs8").Cells(j100, 1).Value   ' MC4
     nVar1 = Sheets("Pairs8").Cells(j100, 5).Value
    
     For i1 = 1 To nVar1
        a1(i1) = Sheets("Pairs8").Cells(j100, 6 + i1).Value
     Next i1
     m1 = 1: m2 = nVar1

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

'    Read Prime Numbers from sheet "Lines72"

2020 m1 = 1: m2 = 64
     s1 = Sheets("Lines72").Cells(j100, m2 + 1).Value    
          
     a2 = 0
     For i1 = m1 To m2
         a1(i1) = Sheets("Lines72").Cells(j100, i1).Value
         If a2 < a1(i1) Then a2 = a1(i1)                    'Determine Maximum
     Next i1
    
     Erase b1
     For i1 = m1 To m2
         b1(a1(i1)) = a1(i1)
     Next i1
    
     n1 = 0: Erase a1                                       'Sort a1
     For i1 = 1 To a2
         If b1(i1) <> 0 Then
            n1 = n1 + 1
            a1(n1) = b1(i1)
         End If
     Next i1
     Return

End Sub

Vorige Pagina About the Author