coan.net: Currently, Logic has 32768 different codes to choose from. Most games seem to finish in 5 or 6 moves. Your "small" logik only has 4096 possibilities (and that's assuming there isn't a reduction in the number of colours). Most games wouldn't go past move 4. "Large" logik would up the number of codes to 262144. Probably requiring 6 to 7 moves.

As for unique logik, with 8 colours and 5 positions, there would be 6720 codes to choose from. Just over 1 in 5 of the possible codes does not duplicate a colour.