' Generates Concentric Magic Squares of order 12 for Prime Numbers
' Optimized for Twin Squares
' Tested with Office 2007 under Windows 7
Sub Priem12a()
Dim a1(2448), a(144), a3(40), a12(144), b1(98929), b(98929), c(144)
y = MsgBox("Locked", vbCritical, "Routine Priem12a")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1: n3 = 0
ShtNm1 = "Pairs6a"
ShtNm2 = "Lines10"
t1 = Timer
For j100 = 10 To 28
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 102).Value
MC10 = Sheets(ShtNm2).Cells(j100, 101).Value
' Read Prime Numbers From Sheet ShtNm1
Pr4 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value 'PairSum
s4 = 2 * Pr4 'MC4
s10 = 5 * Pr4 'MC10
s12 = 6 * Pr4 'MC12
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 5).Value
If nVar < 144 Then GoTo 1000
If MC10 <> s10 Then
y = MsgBox("Conflict in Data", vbCritical, "Read " + ShtNm2 + " " + CStr(j100))
End
End If
Erase b1
For j1 = 1 To nVar
x = Sheets(ShtNm1).Cells(Rcrd1a, 10 + j1).Value
b1(x) = x
Next j1
pMax = Sheets(ShtNm1).Cells(Rcrd1a, 10 + nVar).Value
' Read Concentric Square 10 x 10
For i1 = 1 To 100
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n31 = 1: n32 = 100: GoSub 900 'Remove used primes from available primes
Erase a12
a12(14) = a(1): a12(15) = a(2): a12(16) = a(3): a12(17) = a(4): a12(18) = a(5): a12(19) = a(6): a12(20) = a(7):
a12(21) = a(8): a12(22) = a(9): a12(23) = a(10):
a12(26) = a(11): a12(27) = a(12): a12(28) = a(13): a12(29) = a(14): a12(30) = a(15): a12(31) = a(16): a12(32) = a(17):
a12(33) = a(18): a12(34) = a(19): a12(35) = a(20):
a12(38) = a(21): a12(39) = a(22): a12(40) = a(23): a12(41) = a(24): a12(42) = a(25): a12(43) = a(26): a12(44) = a(27):
a12(45) = a(28): a12(46) = a(29): a12(47) = a(30):
a12(50) = a(31): a12(51) = a(32): a12(52) = a(33): a12(53) = a(34): a12(54) = a(35): a12(55) = a(36): a12(56) = a(37):
a12(57) = a(38): a12(58) = a(39): a12(59) = a(40):
a12(62) = a(41): a12(63) = a(42): a12(64) = a(43): a12(65) = a(44): a12(66) = a(45): a12(67) = a(46): a12(68) = a(47):
a12(69) = a(48): a12(70) = a(49): a12(71) = a(50):
a12(74) = a(51): a12(75) = a(52): a12(76) = a(53): a12(77) = a(54): a12(78) = a(55): a12(79) = a(56): a12(80) = a(57):
a12(81) = a(58): a12(82) = a(59): a12(83) = a(60):
a12(86) = a(61): a12(87) = a(62): a12(88) = a(63): a12(89) = a(64): a12(90) = a(65): a12(91) = a(66): a12(92) = a(67):
a12(93) = a(68): a12(94) = a(69): a12(95) = a(70):
a12(98) = a(71): a12(99) = a(72): a12(100) = a(73): a12(101) = a(74): a12(102) = a(75): a12(103) = a(76): a12(104) = a(77):
a12(105) = a(78): a12(106) = a(79): a12(107) = a(80):
a12(110) = a(81): a12(111) = a(82): a12(112) = a(83): a12(113) = a(84): a12(114) = a(85): a12(115) = a(86): a12(116) = a(87):
a12(117) = a(88): a12(118) = a(89): a12(119) = a(90):
a12(122) = a(91): a12(123) = a(92): a12(124) = a(93): a12(125) = a(94): a12(126) = a(95): a12(127) = a(96): a12(128) = a(97):
a12(129) = a(98): a12(130) = a(99): a12(131) = a(100):
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
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
' Generate Border
For j1 = m1 To m2
If b1(a1(j1)) = 0 Then GoTo 10
If b(a1(j1)) = 0 Then b(a1(j1)) = a1(j1): c(1) = a1(j1) Else GoTo 10
a(1) = a1(j1)
a(5) = Pr4 - a(1): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j2 = m1 To m2
If b1(a1(j2)) = 0 Then GoTo 20
If b(a1(j2)) = 0 Then b(a1(j2)) = a1(j2): c(2) = a1(j2) Else GoTo 20
a(2) = a1(j2)
a(6) = Pr4 - a(2): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j3 = m1 To m2
If b1(a1(j3)) = 0 Then GoTo 30
If b(a1(j3)) = 0 Then b(a1(j3)) = a1(j3): c(3) = a1(j3) Else GoTo 30
a(3) = a1(j3)
a(7) = Pr4 - a(3): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(4) = s4 - a(3) - a(2) - a(1)
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(8) = Pr4 - a(4): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j9 = m1 To m2
If b1(a1(j9)) = 0 Then GoTo 90
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)
a(12) = Pr4 - a(9): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j10 = m1 To m2
If b1(a1(j10)) = 0 Then GoTo 100
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(13) = Pr4 - a(10): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(11) = s4 - a(10) - a(9) - a(1)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 110:
If b1(a(11)) = 0 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(14) = Pr4 - a(11): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
n10 = n10 + 1
If n10 = 1 Then
a12(1) = a(1): a12(2) = a(2): a12(3) = a(3): a12(4) = a(4):
a12(144) = a(5): a12(134) = a(6): a12(135) = a(7): a12(136) = a(8):
a12(13) = a(9): a12(24) = a(12):
a12(25) = a(10): a12(36) = a(13):
a12(37) = a(11): a12(48) = a(14):
n31 = 1: n32 = 14: GoSub 950 'Remove used primes and store in a3()
Erase b, c: GoTo 10
Else
a12(9) = a(4): a12(10) = a(3): a12(11) = a(2): a12(12) = a(1):
a12(141) = a(8): a12(142) = a(7): a12(143) = a(6): a12(133) = a(5):
a12(97) = a(12): a12(108) = a(9):
a12(109) = a(13): a12(120) = a(10):
a12(121) = a(14): a12(132) = a(11):
n31 = 1: n32 = 14: GoSub 950 'Remove used primes and store in a3()
Erase b, c: GoSub 2000 'Complete Border with remaining segments (4 x 1)
If fl1 = 1 Then
GoSub 800: 'Back Check Identical Numbers a12()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 1650 'Print results (squares)
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
End If
Erase a3: n3 = 0: n10 = 0
Erase b1, b, c: GoTo 1000 'Continue with next Magic Sum
Else
GoSub 955 'Reassign removed primes and continue
Erase b, c: GoTo 10
End If
End If
b(c(14)) = 0: c(14) = 0
140 b(c(11)) = 0: c(11) = 0
110 b(c(13)) = 0: c(13) = 0
130 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(12)) = 0: c(12) = 0
120 b(c(9)) = 0: c(9) = 0
90 Next j9
b(c(8)) = 0: c(8) = 0
80 b(c(4)) = 0: c(4) = 0
40 b(c(7)) = 0: c(7) = 0
70 b(c(3)) = 0: c(3) = 0
30 Next j3
b(c(6)) = 0: c(6) = 0
60 b(c(2)) = 0: c(2) = 0
20 Next j2
b(c(5)) = 0: c(5) = 0
50 b(c(1)) = 0: c(1) = 0
10 Next j1
n3 = 0: n10 = 0
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem12a")
End
' Complete Border with remaining segments (4 x 1)
2000 fl1 = 1
For j15 = m1 To m2
If b1(a1(j15)) = 0 Then GoTo 150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(19) = Pr4 - a(15): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
For j16 = m1 To m2
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
a(20) = Pr4 - a(16): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
For j17 = m1 To m2
If b1(a1(j17)) = 0 Then GoTo 170
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)
a(21) = Pr4 - a(17): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(18) = s4 - a(17) - a(16) - a(15)
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(22) = Pr4 - a(18): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
n10 = n10 + 1
If n10 = 3 Then
a12(5) = a(15): a12(6) = a(16): a12(7) = a(17): a12(8) = a(18):
a12(137) = a(19): a12(138) = a(20): a12(139) = a(21): a12(140) = a(22):
n31 = 15: n32 = 22: GoSub 950 'Remove used primes and store in a3()
Erase b, c: GoTo 150
Else
a12(49) = a(15): a12(60) = a(19):
a12(61) = a(16): a12(72) = a(20):
a12(73) = a(17): a12(84) = a(21):
a12(85) = a(18): a12(96) = a(22):
Return
End If
b(c(22)) = 0: c(22) = 0
220 b(c(18)) = 0: c(18) = 0
180 b(c(21)) = 0: c(21) = 0
210 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(20)) = 0: c(20) = 0
200 b(c(16)) = 0: c(16) = 0
160 Next j16
b(c(19)) = 0: c(19) = 0
190 b(c(15)) = 0: c(15) = 0
150 Next j15
fl1 = 0
Return
' Double Check Identical Numbers a12()
800 fl1 = 1
For i1 = 1 To 144
a20 = a12(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 144
If a20 = a12(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Remove used pairs from b1()
900 For i1 = n31 To n32
b1(a(i1)) = 0
b1(Pr4 - a(i1)) = 0 'For Non Symmetrcal Embedded Squares
Next i1
Return
' Remove used pairs from b1()
' Store used primes temporarely in a3()
950 For i1 = n31 To n32
b1(a(i1)) = 0
n3 = n3 + 1: a3(n3) = a(i1)
Next i1
Return
' Reassign primes a3() to available primes b1()
955 For i1 = 1 To n3
b1(a3(i1)) = a3(i1)
Next i1
Erase a3: n3 = 0: n10 = 0
Return
' Print results (lines)
1640 Cells(n9, 122).Select
For i1 = 1 To 144
Cells(n9, i1).Value = a12(i1)
Next i1
Cells(n9, 145).Value = s12
Cells(n9, 146).Value = j100
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 2 Then
n2 = 1: k1 = k1 + 13: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 13
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s12)
i3 = 0
For i1 = 1 To 12
For i2 = 1 To 12
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a12(i3)
Next i2
Next i1
Return
End Sub
