Question 122
A music streaming service offers songs classified into 10 musical genres, so that every song belongs to one and only one genre. The songs are played one after another: the first 17 are chosen by the user, but from the eighteenth on the service automatically decides which song to play. Elisabetta has noticed that, if one ranks the genres by how many times they appear among the last 17 songs played, the new song always belongs to the genre at the top of the ranking or, in case of a tie, to one of the genres tied for first place.
Prove that, however the first 17 songs are chosen, from some point on the proposed songs all belong to the same genre.
Prove that, however the first 17 songs are chosen, from some point on the proposed songs all belong to the same genre.