' Generates Prime Number Composed Magic Squares of Order 13 (Partly Completed)
' Completes Eccentric Square of Order 7 (I7)
' Tested with Office 2007 under Windows 7
Sub PriemI7()
Dim a1(2448), a(169), a7(49), b1(43300), b(43300), c(25)
y = MsgBox("Locked", vbCritical, "Routine PriemI7")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
ShtNm2 = "J1"
t1 = Timer
For j100 = 2 To 66
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 171).Value
' Read Prime Numbers From Sheet Sht1
Pr3 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value
s1 = Sheets(ShtNm1).Cells(Rcrd1a, 5).Value 'MC3
s7 = Sheets(ShtNm1).Cells(Rcrd1a, 3).Value 'MC7
Cntr3 = Sheets(ShtNm1).Cells(Rcrd1a, 6).Value 'Center Element
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
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
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
GoSub 950 'Remove used primes from available primes
s72 = a(59) + a(73) + a(87)
Erase a7
a7(15) = a(57): a7(16) = a(58): a7(17) = a(59): a7(18) = a(60): a7(19) = a(61):
a7(22) = a(70): a7(23) = a(71): a7(24) = a(72): a7(25) = a(73): a7(26) = a(74):
a7(29) = a(83): a7(30) = a(84): a7(31) = a(85): a7(32) = a(86): a7(33) = a(87):
a7(36) = a(96): a7(37) = a(97): a7(38) = a(98): a7(39) = a(99): a7(40) = a(100):
a7(43) = a(109): a7(44) = a(110): a7(45) = a(111): a7(46) = a(112): a7(47) = a(113):
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
a7(5) = a(8): a7(6) = a(9): a7(7) = a(7):
a7(12) = a(2): a7(13) = a(3): a7(14) = a(1):
a7(20) = a(6): a7(21) = a(4):
GoSub 2000 'Determine Diagonal 7 x 7
If fl1 = 0 Then GoTo 5
GoSub 800: If fl1 = 0 Then GoTo 5 'Bachk Check Identical Numbers a7()
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
' GoSub 1200 'Update Input Sheet (Change "J1" => "J2" after Update)
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 PriemI7")
End
' Determine Diagonal 7 x 7
2000 fl1 = 1
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) = (s7 - s72) - 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
For j18 = m1 To m2
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 180
a(18) = a1(j18)
a(19) = Pr3 - a(18): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(20) = s7 - s1 - a(10) - a(15) - a(18)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200:
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(21) = Pr3 - a(20): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
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(23) = Pr3 - a(22): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(24) = s7 - s1 - a(13) - a(16) - a(22)
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(25) = Pr3 - a(24): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a7(1) = a(10): a7(8) = a(14)
a7(9) = a(11): a7(2) = a(15)
a7(3) = a(18): a7(10) = a(19)
a7(4) = a(20): a7(11) = a(21)
a7(35) = a(22): a7(34) = a(23)
a7(28) = a(24): a7(27) = a(25)
a7(41) = a(12): a7(42) = a(16)
a7(49) = a(13): a7(48) = a(17)
Return
b(c(25)) = 0: c(25) = 0
250 b(c(24)) = 0: c(24) = 0
240 b(c(23)) = 0: c(23) = 0
230 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(21)) = 0: c(21) = 0
210 b(c(20)) = 0: c(20) = 0
200 b(c(19)) = 0: c(19) = 0
190 b(c(18)) = 0: c(18) = 0
180 Next j18
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 (selected numbers)
640 For i1 = 1 To 49
Cells(n9, i1).Value = a7(i1)
Next i1
Cells(n9, 50).Value = s7
Cells(n9, 51).Value = Rcrd1a
Return
' Print results (squares)
650 n5 = n5 + 1
If n5 = 4 Then
n5 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s7)
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a7(i3)
Next i2
Next i1
Return
' Double Check Identical Numbers a7()
800 fl1 = 1
For j1 = 1 To 49
a20 = a7(j1)
For j2 = (1 + j1) To 49
If a20 = a7(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Remove used pairs from b1()
950 For j1 = 1 To 169
b1(a(j1)) = 0
Next j1
Return
' Updae Input Sheet
1200
Sheets(ShtNm2).Cells(j100, 31) = a7(1): Sheets(ShtNm2).Cells(j100, 32) = a7(2):
Sheets(ShtNm2).Cells(j100, 33) = a7(3): Sheets(ShtNm2).Cells(j100, 34) = a7(4): Sheets(ShtNm2).Cells(j100, 35) = a7(5):
Sheets(ShtNm2).Cells(j100, 44) = a7(8): Sheets(ShtNm2).Cells(j100, 45) = a7(9):
Sheets(ShtNm2).Cells(j100, 46) = a7(10): Sheets(ShtNm2).Cells(j100, 47) = a7(11): Sheets(ShtNm2).Cells(j100, 48) = a7(12):
Sheets(ShtNm2).Cells(j100, 36) = a7(6): Sheets(ShtNm2).Cells(j100, 37) = a7(7):
Sheets(ShtNm2).Cells(j100, 49) = a7(13): Sheets(ShtNm2).Cells(j100, 50) = a7(14):
Sheets(ShtNm2).Cells(j100, 62) = a7(20): Sheets(ShtNm2).Cells(j100, 63) = a7(21):
Sheets(ShtNm2).Cells(j100, 75) = a7(27): Sheets(ShtNm2).Cells(j100, 76) = a7(28):
Sheets(ShtNm2).Cells(j100, 88) = a7(34): Sheets(ShtNm2).Cells(j100, 89) = a7(35):
Sheets(ShtNm2).Cells(j100, 101) = a7(41): Sheets(ShtNm2).Cells(j100, 102) = a7(42):
Sheets(ShtNm2).Cells(j100, 114) = a7(48): Sheets(ShtNm2).Cells(j100, 115) = a7(49):
Return
End Sub
