The article contains 36 linguistic problems, represented as multiplechoice questions, that were used at the Russkij Medvezhonok linguistic competition for school students. The problems deal with ambiguity at all levels of the language: polysemy, various types of lexical homonymy (full and partial homonyms, homographs, homophones), syntactic ambiguity, etc. In some of the problems, ambiguity is explicitly named, but in most cases it must be discovered by the solvers. It is the surprise factor that makes such problems useful, since the ability to find an unexpected interpretation of a text is a very useful skill. Many problems are based on quotations from prose and poetry and often contain wordplay of various kinds, ambiguity being one of the main sources of humour. Polysemy constitutes one of the greatest challenges for natural language processing, too, and this is demonstrated in the article by several examples of machine translation system failure. The article has three sections with problems for elementary, secondary and high school students. Each problem is supplied with the answer, its detailed explanation, and sometimes additional linguistically relevant information that can be used in lessons, elective courses, or linguistic skill workshops.