My only comment is that 6 or 9 can be the middle number as long as the number still has 2,3,4,5 or 7 anywhere else in the number. I think I understand what you mean though, with managing symetric numbers, you multiplied the symetric number by 3/5 to eliminate 6 and 9 in the middle on odd numbers of digits. If so then you have the same thing I do. As for the other numbers, I worked it out for 80, 890 and 9400 to check my math then started using the equations.