' Generates Concentric (Semi) Latin (Diagonal) Squares of order 5
' Tested with Office 2007 under Windows 7
Sub SemiLat5b()
Dim a(25), a1(5), b(5), n52(10)
y = MsgBox("Locked", vbExclamation, "Routine SemiLat5b")
End
n1 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 5: s1 = 10: Pr5 = 2 * s1 / 5
a1(1) = 0: a1(2) = 1: a1(3) = 2: a1(4) = 3: a1(5) = 4
Sheets("Klad1").Select
t1 = Timer
a(13) = 2
For j25 = m1 To m2 'a(25)
a(25) = a1(j25)
For j24 = m1 To m2 'a(24)
a(24) = a1(j24)
If a(24) = a(25) Then GoTo 240
For j23 = m1 To m2 'a(23)
a(23) = a1(j23)
If a(23) = a(24) Or a(23) = a(25) Then GoTo 230
For j22 = m1 To m2 'a(22)
a(22) = a1(j22)
If a(22) = a(23) Or a(22) = a(24) Or a(22) = a(25) Then GoTo 220
a(21) = s1 - a(22) - a(23) - a(24) - a(25)
a(1) = Pr5 - a(25): a(2) = Pr5 - a(22): a(3) = Pr5 - a(23): a(4) = Pr5 - a(24): a(5) = Pr5 - a(21)
For j20 = m1 To m2 'a(20)
a(20) = a1(j20)
For j19 = m1 To m2 'a(19)
a(19) = a1(j19)
If a(19) = a(20) Then GoTo 190
For j18 = m1 To m2 'a(18)
a(18) = a1(j18)
If a(18) = a(19) Or a(18) = a(20) Then GoTo 180
a(17) = 0.6 * s1 - a(18) - a(19)
If a(17) = a(18) Or a(17) = a(19) Or a(17) = a(20) Then GoTo 180
a(16) = Pr5 - a(20)
a(7) = Pr5 - a(19): a(8) = Pr5 - a(18): a(9) = Pr5 - a(17):
a(14) = 0.8 * s1 - a(18) - 2 * a(19)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 180
a(12) = Pr5 - a(14)
For j15 = m1 To m2 'a(15)
a(15) = a1(j15)
If a(15) = a(12) Or a(15) = a(13) Or a(15) = a(14) Then GoTo 180
a(11) = Pr5 - a(15)
a(10) = 0.6 * s1 - a(15) - a(20) + a(21) - a(25)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 150
a(6) = Pr5 - a(10)
b(1) = a(10): b(2) = a(9): b(3) = a(8): b(4) = a(7): b(5) = a(6):
GoSub 300: If fl1 = 0 Then GoTo 150
' Check Columns
b(1) = a(5): b(2) = a(10): b(3) = a(15): b(4) = a(20): b(5) = a(25):
GoSub 500: If fl1 = 0 Then GoTo 150
b(1) = a(4): b(2) = a(9): b(3) = a(14): b(4) = a(19): b(5) = a(24):
GoSub 500: If fl1 = 0 Then GoTo 150
b(1) = a(3): b(2) = a(8): b(3) = a(13): b(4) = a(18): b(5) = a(23):
GoSub 500: If fl1 = 0 Then GoTo 150
b(1) = a(2): b(2) = a(7): b(3) = a(12): b(4) = a(17): b(5) = a(22):
GoSub 500: If fl1 = 0 Then GoTo 150
b(1) = a(1): b(2) = a(6): b(3) = a(11): b(4) = a(16): b(5) = a(21):
GoSub 500: If fl1 = 0 Then GoTo 150
' Check Latin Diagonals (Option)
' GoSub 400: If fl1 = 0 Then GoTo 150 'Latin Main Diagonals
' n9 = n9 + 1: Cells(1, 27) = n9 'Counting
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
150 Next j15
180 Next j18
190 Next j19
200 Next j20
220 Next j22
230 Next j23
240 Next j24
250 Next j25
t2 = Timer
t10 = Str(t2 - t1) + " sec, " + Str(n9) + " Solutions"
y = MsgBox(t10, vbInformation, "Routine SemiLat5b")
End
' Check Diagonals
400 fl1 = 1
b(1) = a(1): b(2) = a(7): b(3) = a(13): b(4) = a(19): b(5) = a(25):
GoSub 300: If fl1 = 0 Then Return
b(1) = a(5): b(2) = a(9): b(3) = a(13): b(4) = a(17): b(5) = a(21):
GoSub 300: If fl1 = 0 Then Return
Return
300 fl1 = 1
For i1 = 1 To 5
b2 = b(i1)
For i2 = (1 + i1) To 5
If b2 = b(i2) Then fl1 = 0: Return
Next i2
Next i1
Return
' Check Columns
500 fl1 = 1
' Check Magic Constant
If b(1) + b(2) + b(3) + b(4) + b(5) <> s1 Then fl1 = 0: Return
Return
' Limitation for Prime Number Magic Squares (Balanced Series)
' Count 1, 2, 3, 4, 5
Erase n52
For i1 = 1 To 5
n52(b(i1) + 1) = n52(b(i1) + 1) + 1
Next i1
' Check Valid Combinations
fl1 = 0
If n52(1) = 2 And n52(3) = 1 And n52(5) = 2 Then fl1 = 1: Return
If n52(1) = 1 And n52(2) = 1 And n52(3) = 1 And n52(4) = 1 And n52(5) = 1 Then fl1 = 1: Return
If n52(2) = 2 And n52(3) = 1 And n52(4) = 2 Then fl1 = 1: Return
If n52(1) = 1 And n52(3) = 3 And n52(5) = 1 Then fl1 = 1: Return
If n52(2) = 1 And n52(3) = 3 And n52(4) = 1 Then fl1 = 1: Return
If n52(3) = 5 Then fl1 = 1: Return
Return
' Print results (selected numbers)
640 ''Cells(n9, 26).Select
For i1 = 1 To 25
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 26).Value = n9
Cells(1, 27).Value = n9
Return
' Print results (squares)
650 n1 = n1 + 1
If n1 = 5 Then
n1 = 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 = n9
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
End Sub
