  Math is widely considered as a powerful tool and its strong appeal depends on
the high level of abstraction it allows in modelling a huge number of
heterogeneous phenomena and problems, spanning from the static of buildings to
the flight of swarms. As further proof, Gardner's and Carroll's problems have
been intensively employed in a number of selection methods and job interviews.
Despite the mathematical background, these problems are based on, several
solutions and explanations are given in a trivial way. This work proposes a
thorough investigation of this framework, as a whole. The results of such study
are three mathematical formulations that express the understood mathematical
relationship in these well-known riddles. The proposed formulas are of help in
the formalization of the solutions, which have been proven to be less
time-taking when compared to the well-known classic ones, that look more
heuristic than rigorous.
