' Generates Sets of Semi Magic Squares of order 4
' For Associated Magic Squares of order 8 based on Twin Pairs

' Tested with Office 2007 under Windows 7

```Sub Priem4a()

Dim a1(1172), a(32), b1(23967), b(23967), c(32)

y = MsgBox("Locked", vbCritical, "Routine Priem4a")
End

n2 = 0: n3 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs8"

t1 = Timer

For j100 = 2 To 7505

'   Define variables                                         Pairs6

Pr4 = Sheets(ShtNm1).Cells(j100, 1).Value
s1 = 2 * Pr4
nVar1 = Sheets(ShtNm1).Cells(j100, 5).Value             '5
If nVar1 < 64 Then GoTo 1000

'   Read Prime Numbers From sheet ShtNm1

For i1 = 1 To nVar1
a1(i1) = Sheets(ShtNm1).Cells(j100, 6 + i1).Value  '10 + i1
Next i1
m1 = 1: m2 = nVar1

Erase b1

m1 = 1: m2 = nVar1

Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1

'   Generate squares

a17 = 2: n10 = 0

For j16 = m1 To m2                                          'a(16)
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)

x = Pr4 - a(16): If b(x) = 0 Then b(x) = x: c(32) = x Else GoTo 320

a(5) = a(16) - a17
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

x = Pr4 - a(5): If b(x) = 0 Then b(x) = x: c(21) = x Else GoTo 210

For j15 = m1 To m2                                          'a(15)
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)

x = Pr4 - a(15): If b(x) = 0 Then b(x) = x: c(31) = x Else GoTo 310

a(6) = a(15) - a17
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

x = Pr4 - a(6): If b(x) = 0 Then b(x) = x: c(22) = x Else GoTo 220

For j14 = m1 To m2                                          'a(14)
If b1(a1(j14)) = 0 Then GoTo 140
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)

x = Pr4 - a(14): If b(x) = 0 Then b(x) = x: c(30) = x Else GoTo 300

a(13) = s1 - a(14) - a(15) - a(16)
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

x = Pr4 - a(13): If b(x) = 0 Then b(x) = x: c(29) = x Else GoTo 290

a(8) = s1 - a(14) - a(15) - a(16) + a17
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

x = Pr4 - a(8): If b(x) = 0 Then b(x) = x: c(24) = x Else GoTo 240

a(7) = a(14) + a17
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

x = Pr4 - a(7): If b(x) = 0 Then b(x) = x: c(23) = x Else GoTo 230

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)

x = Pr4 - a(12): If b(x) = 0 Then b(x) = x: c(28) = x Else GoTo 280

a(9) = -a(12) + a(14) + a(15)
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

x = Pr4 - a(9): If b(x) = 0 Then b(x) = x: c(25) = x Else GoTo 250

a(4) = -a(12) + a(14) + a(15) - a17
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

x = Pr4 - a(4): If b(x) = 0 Then b(x) = x: c(20) = x Else GoTo 200

a(1) = a(12) + a17
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

x = Pr4 - a(1): If b(x) = 0 Then b(x) = x: c(17) = x Else GoTo 170

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)

x = Pr4 - a(11): If b(x) = 0 Then b(x) = x: c(27) = x Else GoTo 270

a(10) = s1 - a(11) - a(14) - a(15)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100

x = Pr4 - a(10): If b(x) = 0 Then b(x) = x: c(26) = x Else GoTo 260

a(3) = s1 - a(11) - a(14) - a(15) - a17
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

x = Pr4 - a(3): If b(x) = 0 Then b(x) = x: c(19) = x Else GoTo 190

a(2) = a(11) + a17
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

x = Pr4 - a(2): If b(x) = 0 Then b(x) = x: c(18) = x Else GoTo 180

'                           Exclude solutions with identical numbers (Back Check)

'                           GoSub 800: If fl1 = 0 Then GoTo 5

n10 = n10 + 1
'                           n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)

GoSub 900              'Remove used primes from available primes (option)
Erase b, c: GoTo 160
5

b(c(18)) = 0: c(18) = 0
180 b(c(2)) = 0: c(2) = 0
20  b(c(19)) = 0: c(19) = 0
190 b(c(3)) = 0: c(3) = 0
30  b(c(26)) = 0: c(26) = 0
260 b(c(10)) = 0: c(10) = 0
100 b(c(27)) = 0: c(27) = 0
270 b(c(11)) = 0: c(11) = 0
110 Next j11

b(c(17)) = 0: c(17) = 0
170 b(c(1)) = 0: c(1) = 0
10  b(c(20)) = 0: c(20) = 0
200 b(c(4)) = 0: c(4) = 0
40  b(c(25)) = 0: c(25) = 0
250 b(c(9)) = 0: c(9) = 0
90  b(c(28)) = 0: c(28) = 0
280 b(c(12)) = 0: c(12) = 0
120 Next j12

b(c(23)) = 0: c(23) = 0
230 b(c(7)) = 0: c(7) = 0
70  b(c(24)) = 0: c(24) = 0
240 b(c(8)) = 0: c(8) = 0
80  b(c(29)) = 0: c(29) = 0
290 b(c(13)) = 0: c(13) = 0
130 b(c(30)) = 0: c(30) = 0
300 b(c(14)) = 0: c(14) = 0
140 Next j14

b(c(22)) = 0: c(22) = 0
220 b(c(6)) = 0: c(6) = 0
60  b(c(31)) = 0: c(31) = 0
310 b(c(15)) = 0: c(15) = 0
150 Next j15

b(c(21)) = 0: c(21) = 0
210 b(c(5)) = 0: c(5) = 0
50  b(c(32)) = 0: c(32) = 0
320 b(c(16)) = 0: c(16) = 0
160 Next j16

n10 = 0
1000  Next j100

t2 = Timer

t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem4a")

End

'   Print results (selected numbers)

640 For i1 = 1 To 16
Cells(n9, i1).Value = a(i1)
Next i1

Return

'   Print results (squares)

650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 5: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If

Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(s1) + ", " + CStr(n10)

i3 = 0
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1

Return

'   Exclude solutions with identical numbers

800 fl1 = 1
For j1 = 1 To 16
a2 = a(j1)
For j2 = (1 + j1) To 16
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return

'   Remove used primes from available primes

900 For i1 = 1 To 16
b1(a(i1)) = 0
b1(Pr4 - a(i1)) = 0
Next i1
Return

End Sub
```