Characteristics of the medium response:
The response shows some suggestion of a method for being exhaustive, but shows no recognition that this feature is present or that it is needed.
There may also be explicit statements to the effect that "I couldn't find any more."
An answer qualifies as medium if it presents a proof of some important part of the problem — for example, that the number of towers must be even because every tower has exactly one "opposite" by interchanging the colors.
Characteristics of the low response:
The letter describes one or more methods for generating new towers, but fails to deal with the question of devising a method that will exhaustively produce all possible towers, and shows no recognition of the need for such a method.