' Constructs 9 x 9 Concentric Magic Squares (Prime Numbers)
' Optimized for Sophie Germain Primes
' Tested with Office 2007 under Windows 7
Sub Priem9a1
Dim a1(2448), a(169), a9(100), b1(174299), b(174299), c(100)
y = MsgBox("Locked", vbCritical, "Routine Priem9a1")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs2"
ShtNm2 = "Lines7"
t1 = Timer
For j100 = 2 To 10
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 51).Value
MC7 = Sheets(ShtNm2).Cells(j100, 50).Value
' Read Prime Numbers From Sheet ShtNm1
Pr3 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value 'PairSum
Cntr3 = Pr3 / 2 'Center
s3 = 3 * Cntr3 'MC3
s7 = 7 * Cntr3 'MC7
s1 = 9 * Cntr3 'MC9
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
If nVar < 81 Then GoTo 1000
If MC7 <> s7 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 Concentric Square 7 x 7
For i1 = 1 To 49
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n32 = 49: GoSub 950 'Remove used primes from available primes
Erase a9
a9(11) = a(1): a9(12) = a(2): a9(13) = a(3): a9(14) = a(4):
a9(15) = a(5): a9(16) = a(6): a9(17) = a(7):
a9(20) = a(8): a9(21) = a(9): a9(22) = a(10): a9(23) = a(11):
a9(24) = a(12): a9(25) = a(13): a9(26) = a(14):
a9(29) = a(15): a9(30) = a(16): a9(31) = a(17): a9(32) = a(18):
a9(33) = a(19): a9(34) = a(20): a9(35) = a(21):
a9(38) = a(22): a9(39) = a(23): a9(40) = a(24): a9(41) = a(25):
a9(42) = a(26): a9(43) = a(27): a9(44) = a(28):
a9(47) = a(29): a9(48) = a(30): a9(49) = a(31): a9(50) = a(32):
a9(51) = a(33): a9(52) = a(34): a9(53) = a(35):
a9(56) = a(36): a9(57) = a(37): a9(58) = a(38): a9(59) = a(39):
a9(60) = a(40): a9(61) = a(41): a9(62) = a(42):
a9(65) = a(43): a9(66) = a(44): a9(67) = a(45): a9(68) = a(46):
a9(69) = a(47): a9(70) = a(48): a9(71) = a(49):
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
' Determine Border
For j81 = m2 To m1 Step -1 'a9(81)
If b(a1(j81)) = 0 Then b(a1(j81)) = a1(j81): c(81) = a1(j81) Else GoTo 810
a9(81) = a1(j81)
a9(1) = Pr3 - a9(81): If b(a9(1)) = 0 Then b(a9(1)) = a9(1): c(1) = a9(1) Else GoTo 10
For j73 = j81 - 1 To m1 Step -1 'a9(73)
If b(a1(j73)) = 0 Then b(a1(j73)) = a1(j73): c(73) = a1(j73) Else GoTo 730
a9(73) = a1(j73)
a9(9) = Pr3 - a9(73): If b(a9(9)) = 0 Then b(a9(9)) = a9(9): c(9) = a9(9) Else GoTo 90
For j80 = m2 To m1 Step -1 'a9(80)
If b(a1(j80)) = 0 Then b(a1(j80)) = a1(j80): c(80) = a1(j80) Else GoTo 800
a9(80) = a1(j80)
a9(8) = Pr3 - a9(80): If b(a9(8)) = 0 Then b(a9(8)) = a9(8): c(8) = a9(8) Else GoTo 80
For j79 = j80 - 1 To m1 Step -1 'a9(79)
If b(a1(j79)) = 0 Then b(a1(j79)) = a1(j79): c(79) = a1(j79) Else GoTo 790
a9(79) = a1(j79)
a9(7) = Pr3 - a9(79): If b(a9(7)) = 0 Then b(a9(7)) = a9(7): c(7) = a9(7) Else GoTo 70
For j78 = j79 - 1 To m1 Step -1 'a9(78)
If b(a1(j78)) = 0 Then b(a1(j78)) = a1(j78): c(78) = a1(j78) Else GoTo 780
a9(78) = a1(j78)
a9(6) = Pr3 - a9(78): If b(a9(6)) = 0 Then b(a9(6)) = a9(6): c(6) = a9(6) Else GoTo 60
For j77 = j78 - 1 To m1 Step -1 'a9(77)
If b(a1(j77)) = 0 Then b(a1(j77)) = a1(j77): c(77) = a1(j77) Else GoTo 770
a9(77) = a1(j77)
a9(5) = Pr3 - a9(77): If b(a9(5)) = 0 Then b(a9(5)) = a9(5): c(5) = a9(5) Else GoTo 50
For j76 = j77 - 1 To m1 Step -1 'a9(76)
If b(a1(j76)) = 0 Then b(a1(j76)) = a1(j76): c(76) = a1(j76) Else GoTo 760
a9(76) = a1(j76)
a9(4) = Pr3 - a9(76): If b(a9(4)) = 0 Then b(a9(4)) = a9(4): c(4) = a9(4) Else GoTo 40
For j75 = j76 - 1 To m1 Step -1 'a9(75)
If b(a1(j75)) = 0 Then b(a1(j75)) = a1(j75): c(75) = a1(j75) Else GoTo 750
a9(75) = a1(j75)
a9(3) = Pr3 - a9(75): If b(a9(3)) = 0 Then b(a9(3)) = a9(3): c(3) = a9(3) Else GoTo 30
a9(74) = s1 - a9(73) - a9(75) - a9(76) - a9(77) - a9(78) - a9(79) - a9(80) - a9(81)
If a9(74) < a1(m1) Or a9(74) > a1(m2) Then GoTo 740
If b1(a9(74)) = 0 Then GoTo 740
If a9(74) > a9(75) Then GoTo 740
If b(a9(74)) = 0 Then b(a9(74)) = a9(74): c(74) = a9(74) Else GoTo 740
a9(2) = Pr3 - a9(74): If b(a9(2)) = 0 Then b(a9(2)) = a9(2): c(2) = a9(2) Else GoTo 20
For j72 = m2 To m1 Step -1 'a9(72)
If b(a1(j72)) = 0 Then b(a1(j72)) = a1(j72): c(72) = a1(j72) Else GoTo 720
a9(72) = a1(j72)
a9(64) = Pr3 - a9(72): If b(a9(64)) = 0 Then b(a9(64)) = a9(64): c(64) = a9(64) Else GoTo 640
For j63 = j72 - 1 To m1 Step -1 'a9(63)
If b(a1(j63)) = 0 Then b(a1(j63)) = a1(j63): c(63) = a1(j63) Else GoTo 630
a9(63) = a1(j63)
a9(55) = Pr3 - a9(63): If b(a9(55)) = 0 Then b(a9(55)) = a9(55): c(55) = a9(55) Else GoTo 550
For j54 = j63 - 1 To m1 Step -1 'a9(54)
If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
a9(54) = a1(j54)
a9(46) = Pr3 - a9(54): If b(a9(46)) = 0 Then b(a9(46)) = a9(46): c(46) = a9(46) Else GoTo 460
For j45 = j54 - 1 To m1 Step -1 'a9(45)
If b(a1(j45)) = 0 Then b(a1(j45)) = a1(j45): c(45) = a1(j45) Else GoTo 450
a9(45) = a1(j45)
a9(37) = Pr3 - a9(45): If b(a9(37)) = 0 Then b(a9(37)) = a9(37): c(37) = a9(37) Else GoTo 370
For j36 = j45 - 1 To m1 Step -1 'a9(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a9(36) = a1(j36)
a9(28) = Pr3 - a9(36): If b(a9(28)) = 0 Then b(a9(28)) = a9(28): c(28) = a9(28) Else GoTo 280
For j27 = j36 - 1 To m1 Step -1 'a9(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a9(27) = a1(j27)
a9(19) = Pr3 - a9(27): If b(a9(19)) = 0 Then b(a9(19)) = a9(19): c(19) = a9(19) Else GoTo 190
a9(18) = s1 - a9(9) - a9(27) - a9(36) - a9(45) - a9(54) - a9(63) - a9(72) - a9(81)
If a9(18) < a1(m1) Or a9(18) > a1(m2) Then GoTo 180
If b1(a9(18)) = 0 Then GoTo 180
If a9(18) > a9(27) Then GoTo 180
If b(a9(18)) = 0 Then b(a9(18)) = a9(18): c(18) = a9(18) Else GoTo 180
a9(10) = Pr3 - a9(18): If b(a9(10)) = 0 Then b(a9(10)) = a9(10): c(10) = a9(10) Else GoTo 100
' Exclude solutions with identical numbers (Back Check)
GoSub 1800: If fl1 = 0 Then GoTo 5
' n9 = n9 + 1: GoSub 2640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 2650 'Print results (squares)
Erase b1, 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(74)) = 0: c(74) = 0
740 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(9)) = 0: c(9) = 0
90 b(c(73)) = 0: c(73) = 0
730 Next j73
b(c(1)) = 0: c(1) = 0
10 b(c(81)) = 0: c(81) = 0
810 Next j81
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem9a2")
End
' Double Check Identical Numbers a9()
1800 fl1 = 1
For i1 = 1 To 81
a20 = a9(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 81
If a20 = a9(i2) Then fl1 = 0: Return
Next i2
1810 Next i1
Return
' Remove used pairs from b1()
950 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
' Print results (selected numbers)
2645 For i1 = 1 To 81
Cells(n9, i1).Value = a9(i1)
Next i1
Cells(n9, 82).Select
Cells(n9, 82).Value = s1
Cells(n9, 83).Value = Rcrd1a
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 3 Then
n2 = 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(s1)
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
End Sub
