' Generates SelfOrthogonal Latin Diagonal Squares (8 x 8)
' Based on Idempotent Squares (Permutations)
' Tested with Office 365 under Windows 11
Sub SelfOrth8c()
Dim a1(8), a2(64), a(64)
Dim b(8), s(32)
y = MsgBox("Locked", vbCritical, "Routine SelfOrth8a")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
s1 = 28: s2 = 7: s4 = 14
Sheets("Klad1").Select
t1 = Timer
For j100 = 1 To 384 'Idemppotent Squares (1 To 384: Associated)
Cells(2, 1).Value = j100
For i1 = 1 To 64
a2(i1) = Sheets("BaseLns8").Cells(j100, i1).Value
Next i1
For j200 = 1 To 40320 'Series order 8
For i1 = 1 To 8
a1(i1) = Sheets("MgcLns8").Cells(j200, i1).Value
Next i1
For i1 = 1 To 64
i2 = a2(i1) + 1 'Index in a1()
a(i1) = a1(i2)
Next i1
'' GoSub 950: If fl1 = 0 Then GoTo 5 'Check Associated
'' GoSub 900: If fl1 = 0 Then GoTo 5 'Check Pan Diagonals
'' GoSub 1050: If fl1 = 0 Then GoTo 5 'Check Complete
GoSub 1300: If fl1 = 0 Then GoTo 5 'Check Center Square (4 x 4)
n9 = n9 + 1: ''GoSub 2650 'Print Squares
Cells(1, 1).Value = n9 'Counting
''End
5
2000 Next j200
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine SelfOrth8c")
End
' Select Pan Magic Squares (Back Check)
900 fl1 = 1
' Pan Diagonals (Weakly Pan Magic)
s(1) = a(1) + a(10) + a(19) + a(28) + a(37) + a(46) + a(55) + a(64)
s(2) = a(2) + a(11) + a(20) + a(29) + a(38) + a(47) + a(56) + a(57)
s(3) = a(3) + a(12) + a(21) + a(30) + a(39) + a(48) + a(49) + a(58)
s(4) = a(4) + a(13) + a(22) + a(31) + a(40) + a(41) + a(50) + a(59)
s(5) = a(5) + a(14) + a(23) + a(32) + a(33) + a(42) + a(51) + a(60)
s(6) = a(6) + a(15) + a(24) + a(25) + a(34) + a(43) + a(52) + a(61)
s(7) = a(7) + a(16) + a(17) + a(26) + a(35) + a(44) + a(53) + a(62)
s(8) = a(8) + a(9) + a(18) + a(27) + a(36) + a(45) + a(54) + a(63)
s(9) = a(8) + a(15) + a(22) + a(29) + a(36) + a(43) + a(50) + a(57)
s(10) = a(7) + a(14) + a(21) + a(28) + a(35) + a(42) + a(49) + a(64)
s(11) = a(6) + a(13) + a(20) + a(27) + a(34) + a(41) + a(56) + a(63)
s(12) = a(5) + a(12) + a(19) + a(26) + a(33) + a(48) + a(55) + a(62)
s(13) = a(4) + a(11) + a(18) + a(25) + a(40) + a(47) + a(54) + a(61)
s(14) = a(3) + a(10) + a(17) + a(32) + a(39) + a(46) + a(53) + a(60)
s(15) = a(2) + a(9) + a(24) + a(31) + a(38) + a(45) + a(52) + a(59)
s(16) = a(1) + a(16) + a(23) + a(30) + a(37) + a(44) + a(51) + a(58)
For j20 = 1 To 16
If s(j20) <> s1 Then fl1 = 0: Exit For
Next j20
Return
' Select Associated Magic Squares (Back Check)
950 fl1 = 1
s(1) = a(1) + a(64): s(9) = a(9) + a(56): s(17) = a(17) + a(48): s(25) = a(25) + a(40):
s(2) = a(2) + a(63): s(10) = a(10) + a(55): s(18) = a(18) + a(47): s(26) = a(26) + a(39):
s(3) = a(3) + a(62): s(11) = a(11) + a(54): s(19) = a(19) + a(46): s(27) = a(27) + a(38):
s(4) = a(4) + a(61): s(12) = a(12) + a(53): s(20) = a(20) + a(45): s(28) = a(28) + a(37):
s(5) = a(5) + a(60): s(13) = a(13) + a(52): s(21) = a(21) + a(44): s(29) = a(29) + a(36):
s(6) = a(6) + a(59): s(14) = a(14) + a(51): s(22) = a(22) + a(43): s(30) = a(30) + a(35):
s(7) = a(7) + a(58): s(15) = a(15) + a(50): s(23) = a(23) + a(42): s(31) = a(31) + a(34):
s(8) = a(8) + a(57): s(16) = a(16) + a(49): s(24) = a(24) + a(41): s(32) = a(32) + a(33):
For j20 = 1 To 32
If s(j20) <> s2 Then fl1 = 0: Exit For
Next j20
Return
' Select Complete Magic Squares
1050 fl1 = 1
s(1) = a(1) + a(37): s(2) = a(2) + a(38): s(3) = a(3) + a(39): s(4) = a(4) + a(40):
s(5) = a(5) + a(33): s(6) = a(6) + a(34): s(7) = a(7) + a(35): s(8) = a(8) + a(36):
s(9) = a(9) + a(45): s(10) = a(10) + a(46): s(11) = a(11) + a(47): s(12) = a(12) + a(48):
s(13) = a(13) + a(41): s(14) = a(14) + a(42): s(15) = a(15) + a(43): s(16) = a(16) + a(44):
s(17) = a(17) + a(53): s(18) = a(18) + a(54): s(19) = a(19) + a(55): s(20) = a(20) + a(56):
s(21) = a(21) + a(49): s(22) = a(22) + a(50): s(23) = a(23) + a(51): s(24) = a(24) + a(52):
s(25) = a(25) + a(61): s(26) = a(26) + a(62): s(27) = a(27) + a(63): s(28) = a(28) + a(64):
s(29) = a(29) + a(57): s(30) = a(30) + a(58): s(31) = a(31) + a(59): s(32) = a(32) + a(60):
For j20 = 1 To 32
If s(j20) <> s2 Then fl1 = 0: Exit For
Next j20
Return
' Check Center Square (4 x 4)
1300 fl1 = 1
s(1) = a(19) + a(20) + a(21) + a(22)
s(2) = a(27) + a(28) + a(29) + a(30)
s(3) = a(35) + a(36) + a(37) + a(38)
s(4) = a(43) + a(44) + a(45) + a(46)
s(5) = a(19) + a(27) + a(35) + a(43)
s(6) = a(20) + a(28) + a(36) + a(44)
s(7) = a(21) + a(29) + a(37) + a(45)
s(8) = a(22) + a(30) + a(38) + a(46)
s(9) = a(19) + a(28) + a(37) + a(46)
s(10) = a(22) + a(29) + a(36) + a(43)
For j20 = 1 To 10
If s(j20) <> s4 Then fl1 = 0: Exit For
Next j20
Return
' Print results (selected numbers)
2645 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 65).Value = n9
Cells(1, 66).Value = n9
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 9: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 9
End If
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
Cells(k1, k2 + 2).Value = j100
Cells(k1, k2 + 3).Value = j200
'' Cells(k1, k2 + 7).Value = s4 'Option
i3 = 0
For i1 = 1 To 8
For i2 = 1 To 8
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
