' Generates SelfOrthogonal Latin Diagonal Squares (7 x 7)
' Based on Idempotent Squares (Permutations)
' Tested with Office 365 under Windows 11
Sub SelfOrth7c()
Dim a1(7), a2(49), a(49)
Dim b(7), s(24)
y = MsgBox("Locked", vbCritical, "Routine SelfOrth7c")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
s1 = 21: s2 = 6
Sheets("Klad1").Select
t1 = Timer
For j100 = 1 To 64 'Idemppotent Squares
For i1 = 1 To 49
a2(i1) = Sheets("BaseLns7").Cells(j100, i1).Value
Next i1
For j200 = 1 To 5040 'Series order 7
For i1 = 1 To 7
a1(i1) = Sheets("MgcLns7").Cells(j200, i1).Value
Next i1
For i1 = 1 To 49
i2 = a2(i1) + 1 'Index in a1()
a(i1) = a1(i2)
Next i1
'' GoSub 900 : If fl1 = 0 Then GoTo 5 'Check Pan Diagonals
'' GoSub 950 : If fl1 = 0 Then GoTo 5 'Check Associated
'' GoSub 1200: If fl1 = 0 Then GoTo 5 'Check Diamond Inlay
'' n9 = n9 + 1: GoSub 2650 'Print Squares
'' n9 = n9 + 1: GoSub 2645 'Print lines
n9 = n9 + 1: Cells(1, 1).Value = n9 'Counting
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 SelfOrth7c")
End
' Select Pan Magic Squares (Back Check)
900 fl1 = 1
' Check Pan Diagonals
b(1) = a(1): b(2) = a(9): b(3) = a(17): b(4) = a(25): b(5) = a(33): b(6) = a(41): b(7) = a(49):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(2): b(2) = a(10): b(3) = a(18): b(4) = a(26): b(5) = a(34): b(6) = a(42): b(7) = a(43):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(3): b(2) = a(11): b(3) = a(19): b(4) = a(27): b(5) = a(35): b(6) = a(36): b(7) = a(44):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(4): b(2) = a(12): b(3) = a(20): b(4) = a(28): b(5) = a(29): b(6) = a(37): b(7) = a(45):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(5): b(2) = a(13): b(3) = a(21): b(4) = a(22): b(5) = a(30): b(6) = a(38): b(7) = a(46):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(6): b(2) = a(14): b(3) = a(15): b(4) = a(23): b(5) = a(31): b(6) = a(39): b(7) = a(47):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(7): b(2) = a(8): b(3) = a(16): b(4) = a(24): b(5) = a(32): b(6) = a(40): b(7) = a(48):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(43): b(2) = a(37): b(3) = a(31): b(4) = a(25): b(5) = a(19): b(6) = a(13): b(7) = a(7):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(44): b(2) = a(38): b(3) = a(32): b(4) = a(26): b(5) = a(20): b(6) = a(14): b(7) = a(1):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(45): b(2) = a(39): b(3) = a(33): b(4) = a(27): b(5) = a(21): b(6) = a(8): b(7) = a(2):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(46): b(2) = a(40): b(3) = a(34): b(4) = a(28): b(5) = a(15): b(6) = a(9): b(7) = a(3):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(47): b(2) = a(41): b(3) = a(35): b(4) = a(22): b(5) = a(16): b(6) = a(10): b(7) = a(4):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(48): b(2) = a(42): b(3) = a(29): b(4) = a(23): b(5) = a(17): b(6) = a(11): b(7) = a(5):
GoSub 860: If fl1 = 0 Then Return
b(1) = a(49): b(2) = a(36): b(3) = a(30): b(4) = a(24): b(5) = a(18): b(6) = a(12): b(7) = a(6):
GoSub 860: If fl1 = 0 Then Return
Return
860 fl1 = 1
For j1 = 1 To 7
b20 = b(j1)
For j2 = (1 + j1) To 7
If b20 = b(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Select Associated Magic Squares (Back Check)
950 fl1 = 1
s(1) = a(1) + a(49): s(2) = a(2) + a(48): s(3) = a(3) + a(47): s(4) = a(4) + a(46)
s(5) = a(5) + a(45): s(6) = a(6) + a(44): s(7) = a(7) + a(43): s(8) = a(8) + a(42)
s(9) = a(9) + a(41): s(10) = a(10) + a(40): s(11) = a(11) + a(39): s(12) = a(12) + a(38)
s(13) = a(13) + a(37): s(14) = a(14) + a(36): s(15) = a(15) + a(35): s(16) = a(16) + a(34)
s(17) = a(17) + a(33): s(18) = a(18) + a(32): s(19) = a(19) + a(31): s(20) = a(20) + a(30)
s(21) = a(21) + a(29): s(22) = a(22) + a(28): s(23) = a(23) + a(27): s(24) = a(24) + a(26)
For j20 = 1 To 24
If s(j20) <> s2 Then fl1 = 0: Exit For
Next j20
Return
' Check Diamond Inlay Order 3 (Center)
1200 fl1 = 1
s(1) = a(23) + a(17) + a(11)
s(2) = a(31) + a(25) + a(19)
s(3) = a(39) + a(33) + a(27)
s(4) = a(27) + a(19) + a(11)
s(5) = a(33) + a(25) + a(17)
s(6) = a(39) + a(31) + a(23)
s(7) = a(23) + a(25) + a(27)
s(8) = a(11) + a(25) + a(39)
s3 = s(1)
For j20 = 1 To 8
If s(j20) <> s3 Then fl1 = 0: Exit For
Next j20
Return
' Print results (selected numbers)
2645 For i1 = 1 To 49
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 50).Value = n9
Cells(1, 51).Value = n9
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
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
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
