MathDB

2

Part of 2015 ITAMO

Problems(1)

10 musical genres, 17 songs by user, the next by an algorithm

Source: ITAMO 2015 p2

9/2/2018
A music streaming service proposes songs classified in 1010 musical genres, so that each song belong to one and only one gender. The songs are played one after the other: the first 1717 are chosen by the user, but starting from the eighteenth the service automatically determines which song to play. Elisabetta has noticed that, if one makes the classification of which genres they appear several times during the last 1717 songs played, the new song always belongs to the genre at the top of the ranking or, in case of same merit, at one of the first genres. Prove that, however, the first 1717 tracks are chosen, from a certain point onwards the songs proposed are all of the same kind.
combinatoricsalgorithm