The paper addresses a possible way of introducing core concepts of Computational Linguistics through problems given at the linguistic contests organized for high school students in Bulgaria and abroad. Following a brief presentation of the foundation and the underlying objective of these contests, we outline some of the types of problems as reflecting the different levels of language processing and the diversity of approaches and tasks to be solved. By presenting the variety of problems given so far through the years, we would like to attract the attention of the academic community to this captivating method through which high school students might be acquainted with the challenges and the main goals of Computational Linguistics (CL) and Natural Language Processing (NLP).