' Generates Eccentric Magic Squares of order 7 for Prime Numbers
' Overlapping Sub Squares
' Tested with Office 2007 under Windows 7
Sub Priem7e()
Dim a1(2448), a(64), a2(25), b1(43291), b(43291), c(64)
y = MsgBox("Locked", vbCritical, "Routine Priem7e")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
ShtNm2 = "Solutions5"
t1 = Timer
For j100 = 2 To 2349
' Read Ultra Magic Square 5 x 5
For i1 = 1 To 25
a2(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
MC5 = Sheets(ShtNm2).Cells(j100, 26).Value
Rcrd7 = Sheets(ShtNm2).Cells(j100, 27).Value
MC7 = 7 * MC5 / 5: Cntr7 = MC5 / 5
GoSub 750 'Transform Ultra Magic Square
GoSub 2000 'Read Pairs
If MC7 <> s1 Then
y = MsgBox("Conflict in Data", vbCritical, "Read Prime Numbers")
End
End If
' Determine Semi Magic Square 3 x 3
Erase b
For i1 = 1 To 25
b(a2(i1)) = a2(i1)
Next i1
For j16 = m1 To m2 'a(16)
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
a(15) = 2 * Cntr7 - a(16): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j10 = m1 To m2 'a(10)
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(9) = 2 * Cntr7 - 0.5 * a(10) - 0.5 * a(16)
If a(9) < a1(m1) Or a(9) > a1(m2) Or Int(a(9)) <> a(9) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = 3 * Cntr7 - a(9) - a(10)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(3) = 2 * Cntr7 - a(10): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 2 * Cntr7 - a(8): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = 2 * Cntr7 - a(9): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
' Complete Square (Determine Pairs)
For j44 = m1 To m2 'a(44)
If b(a1(j44)) = 0 Then b(a1(j44)) = a1(j44): c(44) = a1(j44) Else GoTo 440
a(44) = a1(j44)
a(43) = 2 * Cntr7 - a(44): If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
For j37 = m1 To m2 'a(37)
If b(a1(j37)) = 0 Then b(a1(j37)) = a1(j37): c(37) = a1(j37) Else GoTo 370
a(37) = a1(j37)
a(36) = 2 * Cntr7 - a(37): If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
For j30 = m1 To m2 'a(30)
If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
a(30) = a1(j30)
a(29) = 2 * Cntr7 - a(30): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(23) = 4 * Cntr7 - a(30) - a(37) - a(44)
If a(23) < a1(m1) Or a(23) > a1(m2) Then GoTo 230
If b1(a(23)) = 0 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = 2 * Cntr7 - a(23): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
For j14 = m1 To m2 'a(14)
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)
a(13) = a(14) - a(37) + a(42) - a(43) + a(48)
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(7) = 2 * Cntr7 - a(14): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = 2 * Cntr7 - a(13): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j12 = m1 To m2 'a(12)
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(11) = 4 * Cntr7 - a(12) - a(13) - a(14)
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(5) = 2 * Cntr7 - a(12): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(4) = 2 * Cntr7 - a(11): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
GoSub 850: If fl1 = 0 Then GoTo 35 'Back Check identical numbers a()
n9 = n9 + 1: GoSub 2650 'Print results (squares)
Erase b1, b, c: GoTo 1000 'Print only first square
35 b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 Next j37
b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 Next j44
b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(8)) = 0: c(8) = 0
80 b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(15)) = 0: c(15) = 0
150 b(c(16)) = 0: c(16) = 0
160 Next j16
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem7e")
End
' Transform Ultra Magic Square
750 Erase a
a(17) = a2(13): a(18) = a2(14): a(19) = a2(15): a(20) = a2(11): a(21) = a2(12):
a(24) = a2(18): a(25) = a2(19): a(26) = a2(20): a(27) = a2(16): a(28) = a2(17):
a(31) = a2(23): a(32) = a2(24): a(33) = a2(25): a(34) = a2(21): a(35) = a2(22):
a(38) = a2(3): a(39) = a2(4): a(40) = a2(5): a(41) = a2(1): a(42) = a2(2):
a(45) = a2(8): a(46) = a2(9): a(47) = a2(10): a(48) = a2(6): a(49) = a2(7):
Return
' Back Check identical numbers a()
850 fl1 = 1
For j1 = 1 To 49
a20 = a(j1)
For j2 = (1 + j1) To 49
If a20 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Read Pairs
2000 s1 = Sheets(ShtNm1).Cells(Rcrd7, 3).Value 'MC7
nVar = Sheets(ShtNm1).Cells(Rcrd7, 9).Value
Erase b1
For j1 = 1 To nVar
x = Sheets(ShtNm1).Cells(Rcrd7, 9 + j1).Value
b1(x) = x
Next j1
nMax = Sheets(ShtNm1).Cells(Rcrd7, 9 + nVar).Value
' Remove used pairs from b1()
For j1 = 1 To 25
b1(a2(j1)) = 0
Next j1
' Restore available pairs in a1()
n10 = 0
For j1 = 1 To nMax
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
Return
' Print results (squares)
2650 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(s1)
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
