' Generates Prime Number Composed Magic Squares of order 9
' Associated Corner Squares, Composed Rectangles
' Tested with Office 2007 under Windows 7
Sub Priem9g2()
Dim a1(2448), a(169), a9(81), b1(43300), b(43300), c(81)
y = MsgBox("Locked", vbCritical, "Routine Priem9g2")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1:
ShtNm1 = "Pairs7"
ShtNm2 = "Lines6"
t1 = Timer
For j100 = 2 To 83
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 38).Value
MC6 = Sheets(ShtNm2).Cells(j100, 37).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
s6 = 6 * Cntr3 'MC6
s9 = 9 * Cntr3 'MC9
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
If nVar < 81 Then GoTo 1000
If MC6 <> s6 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 (Associated) Magic Square 6 x 6
For i1 = 1 To 36
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n32 = 36: GoSub 950 'Remove used primes from available primes
Erase a9
a9(31) = a(1): a9(32) = a(2): a9(33) = a(3): a9(34) = a(4): a9(35) = a(5): a9(36) = a(6):
a9(40) = a(7): a9(41) = a(8): a9(42) = a(9): a9(43) = a(10): a9(44) = a(11): a9(45) = a(12):
a9(49) = a(13): a9(50) = a(14): a9(51) = a(15): a9(52) = a(16): a9(53) = a(17): a9(54) = a(18):
a9(58) = a(19): a9(59) = a(20): a9(60) = a(21): a9(61) = a(22): a9(62) = a(23): a9(63) = a(24):
a9(67) = a(25): a9(68) = a(26): a9(69) = a(27): a9(70) = a(28): a9(71) = a(29): a9(72) = a(30):
a9(76) = a(31): a9(77) = a(32): a9(78) = a(33): a9(79) = a(34): a9(80) = a(35): a9(81) = a(36):
Erase a
' 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
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(1) = a(1): a9(2) = a(2): a9(3) = a(3):
a9(10) = a(4): a9(11) = a(5): a9(12) = a(6):
a9(19) = a(7): a9(20) = a(8): a9(21) = a(9):
' Remove used primes a() from available primes b1()
n32 = 9: GoSub 950
Erase b, c: GoTo 2000
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: GoTo 1000 'Not Found, Next j100
2000 'Continue
' Check Main Diagonal, Generate Associated Magic Rectangles 3 x 6
n10 = 0
For j9 = m1 To m2 'a9(9) Main Diagonal
If b1(a1(j9)) = 0 Then GoTo 2090
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 2090
a9(9) = a1(j9)
For j17 = m1 To m2 'a9(17)
If b1(a1(j17)) = 0 Then GoTo 2170
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 2170
a9(17) = a1(j17)
For j25 = m1 To m2 'a9(25)
If b1(a1(j25)) = 0 Then GoTo 2250
If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 2250
a9(25) = a1(j25)
For j8 = m1 To m2 'a(8) Square 1
If b1(a1(j8)) = 0 Then GoTo 2080
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 2080
a9(8) = a1(j8)
a9(7) = s6 / 2 - a9(8) - a9(9)
If a9(7) < a1(m1) Or a9(7) > a1(m2) Then GoTo 2070
If b1(a9(7)) = 0 Then GoTo 2070
If b(a9(7)) = 0 Then b(a9(7)) = a9(7): c(7) = a9(7) Else GoTo 2070
a9(16) = -a9(25) + a9(9) + a9(8)
If a9(16) < a1(m1) Or a9(16) > a1(m2) Then GoTo 2160
If b1(a9(16)) = 0 Then GoTo 2160
If b(a9(16)) = 0 Then b(a9(16)) = a9(16): c(16) = a9(16) Else GoTo 2160
a9(18) = s6 / 2 + a9(25) - a9(17) - a9(9) - a9(8)
If a9(18) < a1(m1) Or a9(18) > a1(m2) Then GoTo 2180
If b1(a9(18)) = 0 Then GoTo 2180
If b(a9(18)) = 0 Then b(a9(18)) = a9(18): c(18) = a9(18) Else GoTo 2180
a9(26) = s6 / 2 - a9(17) - a9(8)
If a9(26) < a1(m1) Or a9(26) > a1(m2) Then GoTo 2260
If b1(a9(26)) = 0 Then GoTo 2260
If b(a9(26)) = 0 Then b(a9(26)) = a9(26): c(26) = a9(26) Else GoTo 2260
a9(27) = -a9(25) + a9(17) + a9(8)
If a9(27) < a1(m1) Or a9(27) > a1(m2) Then GoTo 2270
If b1(a9(27)) = 0 Then GoTo 2270
If b(a9(27)) = 0 Then b(a9(27)) = a9(27): c(27) = a9(27) Else GoTo 2270
For j57 = m1 To m2 'a9(57)
If b1(a1(j57)) = 0 Then GoTo 2570
If b(a1(j57)) = 0 Then b(a1(j57)) = a1(j57): c(57) = a1(j57) Else GoTo 2570
a9(57) = a1(j57)
For j65 = m1 To m2 'a9(65)
If b1(a1(j65)) = 0 Then GoTo 2650
If b(a1(j65)) = 0 Then b(a1(j65)) = a1(j65): c(65) = a1(j65) Else GoTo 2650
a9(65) = a1(j65)
a9(73) = s9 - a9(65) - a9(57) - a9(49) - a9(41) - a9(33) - a9(25) - a9(17) - a9(9)
If a9(73) < a1(m1) Or a9(73) > a1(m2) Then GoTo 2730:
If b1(a9(73)) = 0 Then GoTo 2730
If b(a9(73)) = 0 Then b(a9(73)) = a9(73): c(73) = a9(73) Else GoTo 2730
For j56 = m1 To m2 'a9(56) Square 2
If b1(a1(j56)) = 0 Then GoTo 2560
If b(a1(j56)) = 0 Then b(a1(j56)) = a1(j56): c(56) = a1(j56) Else GoTo 2560
a9(56) = a1(j56)
a9(55) = s6 / 2 - a9(57) - a9(56)
If a9(55) < a1(m1) Or a9(55) > a1(m2) Then GoTo 2550
If b1(a9(55)) = 0 Then GoTo 2550
If b(a9(55)) = 0 Then b(a9(55)) = a9(55): c(55) = a9(55) Else GoTo 2550
a9(64) = -a9(73) + a9(57) + a9(56)
If a9(64) < a1(m1) Or a9(64) > a1(m2) Then GoTo 2640
If b1(a9(64)) = 0 Then GoTo 2640
If b(a9(64)) = 0 Then b(a9(64)) = a9(64): c(64) = a9(64) Else GoTo 2640
a9(66) = s6 / 2 + a9(73) - a9(65) - a9(57) - a9(56)
If a9(66) < a1(m1) Or a9(66) > a1(m2) Then GoTo 2660
If b1(a9(66)) = 0 Then GoTo 2660
If b(a9(66)) = 0 Then b(a9(66)) = a9(66): c(66) = a9(66) Else GoTo 2660
a9(74) = s6 / 2 - a9(65) - a9(56)
If a9(74) < a1(m1) Or a9(74) > a1(m2) Then GoTo 2740
If b1(a9(74)) = 0 Then GoTo 2740
If b(a9(74)) = 0 Then b(a9(74)) = a9(74): c(74) = a9(74) Else GoTo 2740
a9(75) = -a9(73) + a9(65) + a9(56)
If a9(75) < a1(m1) Or a9(75) > a1(m2) Then GoTo 2750
If b1(a9(75)) = 0 Then GoTo 2750
If b(a9(75)) = 0 Then b(a9(75)) = a9(75): c(75) = a9(75) Else GoTo 2750
' Remove used primes a9() from available primes b1()
n32 = 81: GoSub 900
Erase b, c: GoTo 3000
b(c(75)) = 0: c(75) = 0
2750 b(c(74)) = 0: c(74) = 0
2740 b(c(66)) = 0: c(66) = 0
2660 b(c(64)) = 0: c(64) = 0
2640 b(c(55)) = 0: c(55) = 0
2550 b(c(56)) = 0: c(56) = 0
2560 Next j56
b(c(73)) = 0: c(73) = 0
2730 b(c(65)) = 0: c(65) = 0
2650 Next j65
b(c(57)) = 0: c(57) = 0
2570 Next j57
b(c(27)) = 0: c(27) = 0
2270 b(c(26)) = 0: c(26) = 0
2260 b(c(18)) = 0: c(18) = 0
2180 b(c(16)) = 0: c(16) = 0
2160 b(c(7)) = 0: c(7) = 0
2070 b(c(8)) = 0: c(8) = 0
2080 Next j8
b(c(25)) = 0: c(25) = 0
2250 Next j25
b(c(17)) = 0: c(17) = 0
2170 Next j17
b(c(9)) = 0: c(9) = 0
2090 Next j9
Erase b1, b, c: GoTo 1000 'Not Found, Next j100
' Determine 2 Border Squares
3000 Erase a: n10 = 0 'Continue
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 3090
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 3090
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 3080
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 3080
a(8) = a1(j8)
a(7) = s6 / 2 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 3070
If b1(a(7)) = 0 Then GoTo 3070
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 3070
For j6 = m1 To m2 'a(6)
If b1(a1(j6)) = 0 Then GoTo 3060
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 3060
a(6) = a1(j6)
a(3) = -a(6) + a(7) + a(8)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 3030:
If b1(a(3)) = 0 Then GoTo 3030
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 3030
For j5 = m1 To m2 'a(5)
If b1(a1(j5)) = 0 Then GoTo 3050
If b(a1(j5)) = 0 Then b(a1(j5)) = a1(j5): c(5) = a1(j5) Else GoTo 3050
a(5) = a1(j5)
a(4) = s6 / 2 - a(5) - a(6)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 3040
If b1(a(4)) = 0 Then GoTo 3040
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 3040
a(2) = s6 / 2 - a(5) - a(8)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 3020
If b1(a(2)) = 0 Then GoTo 3020
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 3020
a(1) = a(5) + a(6) - a(7)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 3010
If b1(a(1)) = 0 Then GoTo 3010
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 3010
n10 = n10 + 1
If n10 = 1 Then
a9(4) = a(1): a9(5) = a(2): a9(6) = a(3):
a9(13) = a(4): a9(14) = a(5): a9(15) = a(6):
a9(22) = a(7): a9(23) = a(8): a9(24) = a(9):
n32 = 9: GoSub 950 'Remove used primes a() from available primes b1()
Erase b, c: GoTo 3090
Else
a9(28) = a(1): a9(29) = a(2): a9(30) = a(3):
a9(37) = a(4): a9(38) = a(5): a9(39) = a(6):
a9(46) = a(7): a9(47) = a(8): a9(48) = a(9):
GoSub 800 'Double Check Identical Integers a9()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 650 'Print Composed Squares
End If
Erase b1, b, c: GoTo 1000
End If
b(c(1)) = 0: c(1) = 0
3010 b(c(2)) = 0: c(2) = 0
3020 b(c(4)) = 0: c(4) = 0
3040 b(c(5)) = 0: c(5) = 0
3050 Next j5
b(c(3)) = 0: c(3) = 0
3030 b(c(6)) = 0: c(6) = 0
3060 Next j6
b(c(7)) = 0: c(7) = 0
3070 b(c(8)) = 0: c(8) = 0
3080 Next j8
b(c(9)) = 0: c(9) = 0
3090 Next j9
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem9g2")
End
' Print results (squares)
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
' 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
' Remove used pairs from b1()
900 For i1 = 1 To n32
b1(a9(i1)) = 0
Next i1
Return
' Remove used pairs from b1()
950 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
End Sub
