5. Into how many parts can 7 different tangents to a given circle divide the plane? Provide examples for all answers and prove that no others exist.
Solution. 26,27,28,29. To get the correct answer, one should notice that it is possible to consider cases of pairwise parallelism of several lines. For example, no parallel lines, one pair of parallel lines, two pairs of parallel lines, three pairs of parallel lines.

Criteria. -+ - incomplete enumeration, partially correct answer obtained.

$\pm$ - correct answer, but there is an error in the analysis of cases.