# Enhancing logical deduction with math: the rationale behind Gardner and Carroll

## TL;DR

This paper investigates Gardner's and Carroll's mathematical problems, providing formal formulations that improve solution efficiency and rigor compared to traditional heuristic methods.

## Contribution

It introduces three mathematical formulations that formalize the relationships in Gardner's and Carroll's problems, enhancing solution rigor and efficiency.

## Key findings

- Formal mathematical formulas improve solution speed.
- Formulations provide rigorous understanding of classic problems.
- Solutions are less time-consuming than traditional heuristics.

## Abstract

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.