' Generates Pan Magic Squares of order 5 for Prime Numbers (Part I)
' - Inventarisation for Anti Magic Squares or
' - Input (indices) for AntSym1b
' Tested with Office 2007 under Windows 7
Sub AntSym1a()
Dim a1(658), a(81), b1(43300), b(43300), c(81)
Dim PrClr1(25), PrClr2(25) 'Identify Pairs
y = MsgBox("Locked", vbCritical, "Routine AntSym1a")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm2 = "Pairs7"
ShtNm1 = "Solutions5"
Clmn1 = 25
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 111 To 210 ' To be reconsiderd due to improved method
' limitted collection available in AntSym5a
Rcrd1a = Sheets(ShtNm1).Cells(j100, 29).Value
MC9 = Sheets(ShtNm1).Cells(j100, 32).Value
If MC9 <> 0 Then GoTo 1000
' Read Prime Numbers From sheet "Pairs"
s1 = Sheets(ShtNm2).Cells(Rcrd1a, 4).Value 'MC5
Pr5 = Sheets(ShtNm2).Cells(Rcrd1a, 1).Value
Cntr5 = Sheets(ShtNm2).Cells(Rcrd1a, 6).Value 'Center Element
nVar = Sheets(ShtNm2).Cells(Rcrd1a, 9).Value
m1 = 1: m2 = nVar
For i1 = m1 To m2
a1(i1) = Sheets(ShtNm2).Cells(Rcrd1a, i1 + 9).Value
Next i1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
a24 = Sheets(ShtNm1).Cells(j100, Clmn1).Value
m11 = m1
For i1 = m1 To m2
If a24 = a1(i1) Then m11 = i1: Exit For
Next i1
'' For j25 = m1 To m2 'a(25)
'' If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 250
'' a(25) = a1(j25)
a(25) = Cntr5: b(Cntr5) = Cntr5
''a(50) = Pr5 - a(25): If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
For j24 = m11 To m2
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
''a(49) = Pr5 - a(24): If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
For j23 = m1 To m2 'a(23)
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
''a(48) = Pr5 - a(23): If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
For j22 = m1 To m2 'a(22)
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
a(22) = a1(j22)
''a(47) = Pr5 - a(22): If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(21) = s1 - a(22) - a(23) - a(24) - a(25): If a(21) < a1(m1) Or a(21) > a1(m2) Then GoTo 210
If b1(a(21)) = 0 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
''a(46) = Pr5 - a(21): If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
For j20 = m1 To m2 'a(20)
If b(a1(j20)) = 0 Then b(a1(j20)) = a1(j20): c(20) = a1(j20) Else GoTo 200
a(20) = a1(j20)
''a(45) = Pr5 - a(20): If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(5) = -a(20) + a(22) + a(23): 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(30) = Pr5 - a(5): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
For j19 = m1 To m2 'a(19)
If b(a1(j19)) = 0 Then b(a1(j19)) = a1(j19): c(19) = a1(j19) Else GoTo 190
a(19) = a1(j19)
''a(44) = Pr5 - a(19): If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(12) = a(19) + a(20) - a(22): 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(37) = Pr5 - a(12): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(7) = s1 - a(19) - a(20) - a(24) - a(25): 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(32) = Pr5 - a(7): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(4) = -a(19) + a(21) + a(22): 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(29) = Pr5 - a(4): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
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(43) = Pr5 - a(18): If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(14) = s1 - a(18) - a(19) - a(20) - a(24): If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
''a(39) = Pr5 - a(14): If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(11) = a(18) + a(19) - a(21): 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(36) = Pr5 - a(11): If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(6) = s1 - a(18) - a(19) - a(23) - a(24): 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(31) = Pr5 - a(6): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(3) = -a(18) + a(21) + a(25): 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(28) = Pr5 - a(3): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
For j17 = m1 To m2 'a(17)
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 170
a(17) = a1(j17)
''a(42) = Pr5 - a(17): If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(16) = s1 - a(17) - a(18) - a(19) - a(20):
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160:
If b1(a(16)) = 0 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
''a(41) = Pr5 - a(16): If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(15) = a(17) + a(18) - a(25):
If a(15) < a1(m1) Or a(15) > a1(m2) Then GoTo 150:
If b1(a(15)) = 0 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
''a(40) = Pr5 - a(15): If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(13) = s1 - a(17) - a(18) - a(19) - a(23):
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(38) = Pr5 - a(13): If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(10) = s1 - a(17) - a(18) - a(22) - a(23):
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
''a(35) = Pr5 - a(10): If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(9) = s1 - a(16) - a(17) - a(21) - a(22):
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(34) = Pr5 - a(9): If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(8) = s1 - a(16) - a(20) - a(21) - a(25):
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(33) = Pr5 - a(8): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(2) = -a(17) + a(24) + a(25):
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(27) = Pr5 - a(2): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(1) = -a(16) + a(23) + a(24):
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
''a(26) = Pr5 - a(1): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 5
GoSub 900 'Count Pairs
' If n25 > 8 Then GoTo 5
' n9 = n9 + 1: GoSub 650 'Print results (squares)
n9 = n9 + 1: GoSub 640 'Print results (selected indices)
Erase b, c: GoTo 1000 'Print only first square
5
b(c(26)) = 0: c(26) = 0
260 b(c(1)) = 0: c(1) = 0
10 b(c(27)) = 0: c(27) = 0
270 b(c(2)) = 0: c(2) = 0
20 b(c(33)) = 0: c(33) = 0
330 b(c(8)) = 0: c(8) = 0
80 b(c(34)) = 0: c(34) = 0
340 b(c(9)) = 0: c(9) = 0
90 b(c(35)) = 0: c(35) = 0
350 b(c(10)) = 0: c(10) = 0
100 b(c(38)) = 0: c(38) = 0
380 b(c(13)) = 0: c(13) = 0
130 b(c(40)) = 0: c(40) = 0
400 b(c(15)) = 0: c(15) = 0
150 b(c(41)) = 0: c(41) = 0
410 b(c(16)) = 0: c(16) = 0
160 b(c(42)) = 0: c(42) = 0
420 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(28)) = 0: c(28) = 0
280 b(c(3)) = 0: c(3) = 0
30 b(c(31)) = 0: c(31) = 0
310 b(c(6)) = 0: c(6) = 0
60 b(c(36)) = 0: c(36) = 0
360 b(c(11)) = 0: c(11) = 0
110 b(c(39)) = 0: c(39) = 0
390 b(c(14)) = 0: c(14) = 0
140 b(c(43)) = 0: c(43) = 0
430 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(29)) = 0: c(29) = 0
290 b(c(4)) = 0: c(4) = 0
40 b(c(32)) = 0: c(32) = 0
320 b(c(7)) = 0: c(7) = 0
70 b(c(37)) = 0: c(37) = 0
370 b(c(12)) = 0: c(12) = 0
120 b(c(44)) = 0: c(44) = 0
440 b(c(19)) = 0: c(19) = 0
190 Next j19
b(c(30)) = 0: c(30) = 0
300 b(c(5)) = 0: c(5) = 0
50 b(c(45)) = 0: c(45) = 0
450 b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(46)) = 0: c(46) = 0
460 b(c(21)) = 0: c(21) = 0
210 b(c(47)) = 0: c(47) = 0
470 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(48)) = 0: c(48) = 0
480 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(49)) = 0: c(49) = 0
490 b(c(24)) = 0: c(24) = 0
240 Next j24
'' b(c(50)) = 0: c(50) = 0
''500 b(c(25)) = 0: c(25) = 0
''250 Next j25
1000 Erase b, c
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine AntSym1a")
End
' Print results (selected indices)
640
For i1 = m1 To m2
If a1(i1) = Cntr5 Then j25 = i1: Exit For
Next i1
Cells(n9 + 1, 1).Value = j25
Cells(n9 + 1, 2).Value = j24
Cells(n9 + 1, 3).Value = j23
Cells(n9 + 1, 4).Value = j22
Cells(n9 + 1, 5).Value = j20
Cells(n9 + 1, 6).Value = j19
Cells(n9 + 1, 7).Value = j18
Cells(n9 + 1, 8).Value = j17
For i1 = m1 To m2
If a1(i1) = a(15) Then j15 = i1: Exit For
Next i1
Cells(n9 + 1, 9).Value = j15
For i1 = m1 To m2
If a1(i1) = a(14) Then j14 = i1: Exit For
Next i1
Cells(n9 + 1, 10).Value = j14
Cells(n9 + 1, 11).Value = s1
Cells(n9 + 1, 12).Value = Rcrd1a
Cells(n9 + 1, 13).Value = n25
Return
' Print results (squares for further analysis)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 6
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s1)
Cells(k1, k2 + 5).Value = n25 'Pairs
Cells(k1, k2 + 4).Value = n9 'Sequence
i3 = 0
For i1 = 1 To 5
For i2 = 1 To 5
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
If PrClr1(i3) = 1 Then 'HighLight Pairs
Cells(k1 + i1, k2 + i2).Interior.Color = 65535
End If
If PrClr2(i3) = 1 Then 'HighLight Critical Pairs
Cells(k1 + i1, k2 + i2).Font.Color = -16776961
End If
Next i2
Next i1
' Determine Indices
Range(Cells(k1 + 6, k2 + 2), Cells(k1 + 7, k2 + 5)).Font.Color = -4165632
Cells(k1 + 3, k2 + 6).Font.Color = -4165632
For i1 = m1 To m2
If a1(i1) = a(15) Then j15 = i1: Exit For
Next i1
Cells(k1 + 3, k2 + 6).Value = j15
Cells(k1 + 2, k2 + 6).Font.Color = -4165632
For i1 = m1 To m2
If a1(i1) = a(14) Then j14 = i1: Exit For
Next i1
Cells(k1 + 2, k2 + 6).Value = j14
Cells(k1 + 6, k2 + 2).Value = j17
Cells(k1 + 6, k2 + 3).Value = j18
Cells(k1 + 6, k2 + 4).Value = j19
Cells(k1 + 6, k2 + 5).Value = j20
Cells(k1 + 7, k2 + 2).Value = j22
Cells(k1 + 7, k2 + 3).Value = j23
Cells(k1 + 7, k2 + 4).Value = j24
For i1 = m1 To m2
If a1(i1) = Cntr5 Then j25 = i1: Exit For
Next i1
Cells(k1 + 7, k2 + 5).Value = j25
Return
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 50
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 50
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
' Check Pairs
900 fl1 = 1: n25 = 0
Erase PrClr1, PrClr2
For j1 = 1 To 24
a2 = 0.4 * s1 - a(j1) 'Complement
For j2 = (1 + j1) To 24
' If a2 = a(j2) Then fl1 = 0: Return
If a2 = a(j2) Then
n25 = n25 + 1
PrClr1(j1) = 1: PrClr1(j2) = 1
If j1 >= 15 And j2 >= 15 Then
PrClr2(j1) = 1: PrClr2(j2) = 1
End If
End If
Next j2
Next j1
Return
End Sub
