' Generates Composed Magic Squares of order 7 for Prime Numbers
' Associated Magic Corner Squares and - Rectangles
' Tested with Office 2007 under Windows 7
Sub Priem7e3()
Dim a1(2448), a(100), a7(100), b1(121817), b(121817), c(100)
y = MsgBox("Locked", vbCritical, "Routine Priem7e3")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
t1 = Timer
For j101 = 2 To 22
j100 = Sheets("Index7").Cells(j101, 2).Value
' Read Pairs
Pr3 = Sheets(ShtNm1).Cells(j100, 1).Value 'PairSum
nvar = Sheets(ShtNm1).Cells(j100, 9).Value
s1 = 7 * Pr3 / 2
s3 = 3 * Pr3 / 2
s4 = 4 * Pr3 / 2
For j1 = 1 To nvar
x = Sheets(ShtNm1).Cells(j100, 9 + j1).Value
a1(j1) = x: b1(x) = x
Next j1
m1 = 1: m2 = nvar: n10 = 0
If a1(m1) = 1 Then m1 = m1 + 1: m2 = m2 - 1
If m2 <= 49 Then GoTo 1000
' Generate Magic Corner Square 3 x 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 260
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 220
a(8) = a1(j8)
a(7) = s3 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 210:
If b1(a(7)) = 0 Then GoTo 210
a(6) = 4 * s3 / 3 - a(8) - 2 * a(9):
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 210:
If b1(a(6)) = 0 Then GoTo 210
a(5) = s3 / 3:
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 210:
If b1(a(5)) = 0 Then GoTo 210
a(4) = -2 * s3 / 3 + 1 * a(8) + 2 * a(9):
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 210:
If b1(a(4)) = 0 Then GoTo 210
a(3) = -s3 / 3 + 1 * a(8) + 1 * a(9):
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 210:
If b1(a(3)) = 0 Then GoTo 210
a(2) = 2 * s3 / 3 - a(8):
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 210:
If b1(a(2)) = 0 Then GoTo 210
a(1) = 2 * s3 / 3 - a(9):
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 210:
If b1(a(1)) = 0 Then GoTo 210
' Exclude solutions with identical numbers a()
n33 = 9: GoSub 820: If fl1 = 0 Then GoTo 210
' Assign to a7()
a7(1) = a(1): a7(2) = a(2): a7(3) = a(3):
a7(8) = a(4): a7(9) = a(5): a7(10) = a(6):
a7(15) = a(7): a7(16) = a(8): a7(17) = a(9):
' Remove used primes a() from available primes b1()
n32 = 9: GoSub 950
Erase b, c: GoTo 200
210 b(c(8)) = 0: c(8) = 0
220 Next j8
b(c(9)) = 0: c(9) = 0
260 Next j9
Erase b1, b, c: GoTo 1000 'Not Found, Next j101
200 'Continue
' Generate Associated Magic Rectangles 3 x 4
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(1) = Pr3 - a(12): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j11 = m1 To m2 'a(11)
If b1(a1(j11)) = 0 Then GoTo 110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)
a(2) = Pr3 - a(11): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j10 = m1 To m2 'a(10)
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(9) = 2 * Pr3 - a(10) - a(11) - a(12)
If a(9) < a1(m1) Or a(9) > a1(m2) 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) = 5 * Pr3 / 2 - a(10) - a(11) - 2 * a(12)
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(7) = 3 * Pr3 - a(8) - 2 * a(11) - 2 * a(12)
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) = Pr3 - a(7): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = Pr3 - a(8): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(4) = Pr3 - a(9): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = Pr3 - a(10): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
If n10 = 1 Then
a7(25) = s1 - a7(19) - a7(13) - a7(7) - a(12) - a(7) - a(2)
If a7(25) < a1(m1) Or a7(25) > a1(m2) Then GoTo 5:
If b1(a7(25)) = 0 Then GoTo 5
If b(a7(25)) <> 0 Then GoTo 5
End If
n10 = n10 + 1
Select Case n10
Case 1:
a7(4) = a(1): a7(5) = a(2): a7(6) = a(3): a7(7) = a(4):
a7(11) = a(5): a7(12) = a(6): a7(13) = a(7): a7(14) = a(8):
a7(18) = a(9): a7(19) = a(10): a7(20) = a(11): a7(21) = a(12):
n32 = 12: GoSub 950 'Remove used pairs from b1()
Erase b, c: GoTo 120
Case 2:
a7(22) = a(9): a7(23) = a(5): a7(24) = a(1):
a7(29) = a(10): a7(30) = a(6): a7(31) = a(2):
a7(36) = a(11): a7(37) = a(7): a7(38) = a(3):
a7(43) = a(12): a7(44) = a(8): a7(45) = a(4):
n32 = 12: GoSub 950 'Remove used pairs from b1()
Erase b, c: GoTo 2000
End Select
5 b(c(3)) = 0: c(3) = 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 b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(2)) = 0: c(2) = 0
20 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(1)) = 0: c(1) = 0
10 b(c(12)) = 0: c(12) = 0
120 Next j12
Erase b1, b, c: GoTo 1000 'Not Found, Next j101
' Generate Associated Magic Square 4 x 4
2000 'Continue
a(16) = a7(25): b(a(16)) = a(16)
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 2150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 2150
a(15) = a1(j15)
For j14 = m1 To m2 'a(14)
If b1(a1(j14)) = 0 Then GoTo 2140
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 2140
a(14) = a1(j14)
a(13) = s4 - a(14) - a(15) - a(16)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 2130
If b1(a(13)) = 0 Then GoTo 2130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 2130
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 2120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 2120
a(12) = a1(j12)
a(11) = s4 - a(12) - a(15) - a(16)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 2070
If b1(a(11)) = 0 Then GoTo 2070
a(10) = s4 - a(12) - a(14) - a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 2070
If b1(a(10)) = 0 Then GoTo 2070
a(9) = s4 - a(10) - a(11) - a(12)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 2070
If b1(a(9)) = 0 Then GoTo 2070
a(8) = Pr3 - a(9)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 2070
If b1(a(8)) = 0 Then GoTo 2070
a(7) = Pr3 - a(10)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 2070:
If b1(a(7)) = 0 Then GoTo 2070
a(6) = Pr3 - a(11)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 2070:
If b1(a(6)) = 0 Then GoTo 2070
a(5) = Pr3 - a(12)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 2070:
If b1(a(5)) = 0 Then GoTo 2070
a(4) = Pr3 - a(13)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 2070:
If b1(a(4)) = 0 Then GoTo 2070
a(3) = Pr3 - a(14)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 2070:
If b1(a(3)) = 0 Then GoTo 2070
a(2) = Pr3 - a(15)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 2070:
If b1(a(2)) = 0 Then GoTo 2070
a(1) = Pr3 - a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 2070:
If b1(a(1)) = 0 Then GoTo 2070
n33 = 16: GoSub 820
If fl1 = 0 Then GoTo 2070
' Assign a() to a7()
a7(26) = a(15): a7(27) = a(14): a7(28) = a(13):
a7(32) = a(12): a7(33) = a(11): a7(34) = a(10): a7(35) = a(9):
a7(39) = a(8): a7(40) = a(7): a7(41) = a(6): a7(42) = a(5):
a7(46) = a(4): a7(47) = a(3): a7(48) = a(2): a7(49) = a(1):
GoSub 800 'Double Check Identical Integers a7()
If fl1 = 1 Then
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
n9 = n9 + 1: GoSub 1650 'Print results (squares)
End If
Erase b1, b, c: GoTo 1000 'Print only first square
2070 b(c(12)) = 0: c(12) = 0
2120 Next j12
b(c(13)) = 0: c(13) = 0
2130 b(c(14)) = 0: c(14) = 0
2140 Next j14
b(c(15)) = 0: c(15) = 0
2150 Next j15
Erase b1, b, c
1000 Next j101
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem7e3")
End
' Double Check Identical Numbers a7()
800 fl1 = 1
For i1 = 1 To 49
a20 = a7(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 49
If a20 = a7(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Check Identical Numbers a()
820 fl1 = 1
For i1 = 1 To n33
a20 = a(i1)
For i2 = (1 + i1) To n33
If a20 = a(i2) Then fl1 = 0: Return
Next i2
Next i1
Return
' Remove used primes from b1()
950 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
' Print results (lines)
1640 Cells(n9, 13).Select
For i1 = 1 To 49
Cells(n9, i1).Value = a7(i1)
Next i1
Cells(n9, 101).Value = s7
Cells(n9, 102).Value = Rcrd1a
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 4 Then
n2 = 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 = a7(i3)
Next i2
Next i1
Return
End Sub
