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In an overall framework of numerical illiteracy (i.e., innumeracy), mathematical games can provide useful introductory tools to critical thinking and the scientific method to deal with logical and probability problems that arise in everyday life. The work provides a unified framework to a number of puzzles, already spread in several papers. The majority of them are somewhat paradoxical, i.e., of counterintuitive solution, but, in addition to being entertaining, allow us to critically and quantitatively evaluate situations, even subjective ones, related to our lives. Many cases, e.g., the controversial Monty Hall problem, a classical brain teaser, can be tackled intuitively, often with the aid of heuristics or rules of thumb, by using very simple arithmetic. [ABSTRACT FROM AUTHOR]