' Generates Concentric Magic Squares of order 6 for Prime Numbers
' Optimized for Twin Squares
' Tested with Office 2007 under Windows 7
Sub Priem6b2()
Dim a1(2448), a(36), a4(36), b1(105769), b(105769), c(36)
y = MsgBox("Locked", vbCritical, "Routine Priem6b2")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
Sht1 = "Pairs6a"
Sht2 = "Lines4"
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 96
Rcrd1a = Sheets(Sht2).Cells(j100, 20).Value
' Define variables
Pr6 = Sheets(Sht1).Cells(Rcrd1a, 1).Value 'Pair Sum
s1 = Sheets(Sht1).Cells(Rcrd1a, 4).Value 'MC6
nvar = Sheets(Sht1).Cells(Rcrd1a, 5).Value
m1 = 1: m2 = nvar
For i1 = m1 To m2
a1(i1) = Sheets(Sht1).Cells(Rcrd1a, i1 + 10).Value
Next i1
If a1(1) = 1 Then m1 = m1 + 1: m2 = m2 - 1
pMax = a1(m2)
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Read Center Square and remove from Available Primes
' Including Complements for Non Symmetrical Center Squares
For i1 = 1 To 16
a4(i1) = Sheets(Sht2).Cells(j100, i1).Value
b1(a4(i1)) = 0
b1(Pr6 - a4(i1)) = 0
Next i1
Erase a
' Load Center Square
a(8) = a4(1): a(9) = a4(2): a(10) = a4(3): a(11) = a4(4):
a(14) = a4(5): a(15) = a4(6): a(16) = a4(7): a(17) = a4(8):
a(20) = a4(9): a(21) = a4(10): a(22) = a4(11): a(23) = a4(12):
a(26) = a4(13): a(27) = a4(14): a(28) = a4(15): a(29) = a4(16):
Erase a4
' 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
' Determine Border Concentric Square
For j36 = m1 To m2 'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a(36) = a1(j36)
a(1) = s1 / 3 - a(36)
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
For j35 = m1 To m2 'a(35)
If b(a1(j35)) = 0 Then b(a1(j35)) = a1(j35): c(35) = a1(j35) Else GoTo 350
a(35) = a1(j35)
a(5) = s1 / 3 - a(35)
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
For j34 = m1 To m2 'a(34)
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
a(4) = s1 / 3 - a(34)
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
For j33 = m1 To m2 'a(33)
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(3) = s1 / 3 - a(33)
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
For j32 = m1 To m2 'a(32)
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)
a(31) = s1 - a(32) - a(33) - a(34) - a(35) - a(36)
If a(31) < a1(m1) Or a(31) > a1(m2) Then GoTo 310
If b1(a(31)) = 0 Then GoTo 310
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(6) = -2 * s1 / 3 + a(32) + a(33) + a(34) + a(35) + a(36)
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(2) = s1 / 3 - a(32)
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
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(25) = s1 / 3 - a(30)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
For j24 = m1 To m2 'a(24)
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(19) = s1 / 3 - a(24)
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
For j18 = m1 To m2 'a(18)
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 180
a(18) = a1(j18)
a(13) = s1 / 3 - a(18)
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(12) = 2 * s1 / 3 - a(18) - a(24) - a(30) + a(31) - a(36)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(7) = -4 * s1 / 3 + a(18) + a(24) + a(30) + a(32) + a(33) + a(34) + a(35) + 2 * a(36)
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
n9 = n9 + 1
GoSub 2650 'Print results (squares)
' GoSub 2645 'Print results (selected numbers)
Erase b, c: GoTo 1000 'Print only first square
b(c(7)) = 0: c(7) = 0
70 b(c(12)) = 0: c(12) = 0
120 b(c(13)) = 0: c(13) = 0
130 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(19)) = 0: c(19) = 0
190 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(25)) = 0: c(25) = 0
250 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(2)) = 0: c(2) = 0
20 b(c(6)) = 0: c(6) = 0
60 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(3)) = 0: c(3) = 0
30 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(4)) = 0: c(4) = 0
40 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(5)) = 0: c(5) = 0
50 b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(1)) = 0: c(1) = 0
10 b(c(36)) = 0: c(36) = 0
360 Next j36
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem6b2")
End
' Double Check Identical Numbers
800 fl1 = 1
For j1 = 1 To 36
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 36
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
' Print results (selected numbers)
2645 For i1 = 1 To 36
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 37).Select
Cells(n9, 37).Value = s1: Cells(n9, 38).Value = Rcrd1a
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 4 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
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 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Sheets("Pairs6a").Cells(Rcrd1a, 9).Value = "ok"
Return
End Sub
