' 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
