' Generates Anti Symmetric Magic Squares of order 5 for Prime Numbers (Part II)
' Based on indices generated with AntSym1a
' Tested with Office 2007 under Windows 7
Sub AntSym1b()
Dim a1(658), a(81), b1(43300), b(43300), c(81), m(25), s10(8)
y = MsgBox("Locked", vbCritical, "Routine AntSym1b")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm2 = "Pairs7"
ShtNm1 = "Solutions5a" 'Generated indices
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 185
Rcrd1a = Sheets(ShtNm1).Cells(j100, 12).Value
m(25) = Sheets(ShtNm1).Cells(j100, 1).Value:
m(24) = Sheets(ShtNm1).Cells(j100, 2).Value:
m(23) = Sheets(ShtNm1).Cells(j100, 3).Value:
m(22) = Sheets(ShtNm1).Cells(j100, 4).Value
m(20) = Sheets(ShtNm1).Cells(j100, 5).Value:
m(19) = Sheets(ShtNm1).Cells(j100, 6).Value:
m(18) = Sheets(ShtNm1).Cells(j100, 7).Value:
m(17) = Sheets(ShtNm1).Cells(j100, 8).Value
m(15) = Sheets(ShtNm1).Cells(j100, 9).Value:
m(14) = Sheets(ShtNm1).Cells(j100, 10).Value
' 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
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
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
'' b(Cntr5) = Cntr5
For j25 = m(25) To m2 ''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(50) = Pr5 - a(25): If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
For j24 = m(24) To m2 ''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(49) = Pr5 - a(24): If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
For j23 = m(23) To m2 ''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 = m(22) To m2 ''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 = m(20) To m2 ''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
For j19 = m(19) To m2 ''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
For j18 = m(18) To m2 ''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
For j17 = m(17) To m2 ''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
For j15 = m(15) To m2 ''m1 To m2 'a(15)
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(40) = Pr5 - a(15): If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
For j14 = m(14) 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(39) = Pr5 - a(14): If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
For j13 = m1 To m2 'a(13)
If b(a1(j13)) = 0 Then b(a1(j13)) = a1(j13): c(13) = a1(j13) Else GoTo 130
a(13) = a1(j13)
a(38) = Pr5 - a(13): If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
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(37) = Pr5 - a(12): If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(11) = s1 - a(12) - a(13) - a(14) - a(15):
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
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(35) = Pr5 - a(10): If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(9) = a(10) - a(13) + a(15) - a(17) + a(20) - a(21) + a(25):
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(5) = s1 - a(9) - a(13) - a(17) - a(21):
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
a(4) = s1 - a(9) - a(14) - a(19) - a(24):
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 j8 = m1 To m2 'a(8)
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(33) = Pr5 - a(8): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(7) = (s1 - a(8) - a(9) - a(10) + a(11) - a(13) + a(16) - a(19) + a(21) - a(25)) / 2
j7 = Int(a(7)): If j7 <> a(7) Then GoTo 70
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(6) = s1 - a(7) - a(8) - a(9) - a(10):
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) = s1 - a(8) - a(13) - a(18) - a(23):
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
a(2) = s1 - a(7) - a(12) - a(17) - a(22):
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) = s1 - a(2) - a(3) - a(4) - a(5):
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
GoSub 800: If fl1 = 0 Then GoTo 5 ' Identical Numbers (Back Check)
' GoSub 850: If fl2 = 0 Then GoTo 5 ' Pan Diagonals (Option)
GoSub 900 ' Check Pairs
' n9 = n9 + 1: GoSub 650 'Print results (squares)
n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
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(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(32)) = 0: c(32) = 0
320 b(c(7)) = 0: c(7) = 0
70 b(c(33)) = 0: c(33) = 0
330 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(29)) = 0: c(29) = 0
290 b(c(4)) = 0: c(4) = 0
40 b(c(30)) = 0: c(30) = 0
300 b(c(5)) = 0: c(5) = 0
50 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 Next j10
b(c(36)) = 0: c(36) = 0
360 b(c(11)) = 0: c(11) = 0
110 b(c(37)) = 0: c(37) = 0
370 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(38)) = 0: c(38) = 0
380 b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(39)) = 0: c(39) = 0
390 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(40)) = 0: c(40) = 0
400 b(c(15)) = 0: c(15) = 0
150 Next j15
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(43)) = 0: c(43) = 0
430 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(44)) = 0: c(44) = 0
440 b(c(19)) = 0: c(19) = 0
190 Next j19
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 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine AntSym1b")
End
' Print results (selected numbers)
640 ''Cells(n9, 25).Select
For i1 = 1 To 25
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 26).Value = s1 'MC5
Cells(n9, 28).Value = Rcrd1a 'Record
Cells(n9, 29).Value = n25 'Pairs
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 6: 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
i3 = 0
For i1 = 1 To 5
For i2 = 1 To 5
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 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 Pan Diagonals
850 fl2 = 1
s10(1) = a(2) + a(8) + a(14) + a(20) + a(21)
s10(2) = a(3) + a(9) + a(15) + a(16) + a(22)
s10(3) = a(4) + a(10) + a(11) + a(17) + a(23)
s10(4) = a(5) + a(6) + a(12) + a(18) + a(14)
s10(5) = a(22) + a(18) + a(14) + a(10) + a(1)
s10(6) = a(23) + a(19) + a(15) + a(6) + a(2)
s10(8) = a(14) + a(20) + a(11) + a(7) + a(3)
s10(8) = a(15) + a(16) + a(12) + a(8) + a(4)
For j1 = 1 To 8
If s10(j1) <> s1 Then fl2 = 0: Return
Next j1
Return
' Check Pairs
900 fl1 = 1: n25 = 0
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
Next j2
Next j1
Return
End Sub
