Math question involving iTunes playlists

[Garfield226]

For those unaware, iTunes has the capability of "smart playlists," which are playlists that can search your library for certain criteria and pull songs onto (or knock songs off of) themselves automatically. While I could tell it to make a smart playlist with any song with "Jazz" as its genre and iTunes would do that (and always pull new jazz songs on it automatically), many people use these to create a sort of personal radio station. Which is where my question comes in.

The setup: Assume I have four smart playlists, which we'll call A, B, C and D. Playlist A includes any song rated five stars that hasn't been played in the past day. B includes any song rated four stars that hasn't been played in the past three days. C is any song rated three stars that hasn't been played in the past five days. D is any song rated two stars that hasn't been played in the past seven days.

For example, if I play a five-star song on playlist A, after I've listened to it, it drops off playlist A for one day and jumps back onto the playlist automatically after its quarantined time is up.

Tying it all together is another master playlist that selects songs randomly from the other four. The only function of this playlist is to randomly select songs from the other four, but if the song isn't on A, B, C or D, it won't be selected.

The question: What's the minimum amount of music I could have distributed over which playlists to have uninterrupted music? Bonus if there's a formula.

Obviously having 24 hours on playlist A is enough, or three days-worth on B, and so on. But the randomness factor should come into play at some point, right? As well as the fact that time is passing while each song is playing?

I have a feeling this isn't terribly clear. Ask and I'll clarify.

[Punoqllads]

A 3 minute song on list A is worth 3 minutes per day, but a 3 minute song on list B is worth only 1 minute per day, since it can only be played once every 3 days. So, A + B/3 + C/5 + D/7 must be greater than or equal to 24 hours to leave no gaps. If playlist A is shorter than 24 hours then the amount of time needed on the other playlists would push the total amount of time over 24 hours.

[Chronos]

Tying it all together is another master playlist that selects songs randomly from the other four. The only function of this playlist is to randomly select songs from the other four, but if the song isn't on A, B, C or D, it won't be selected.To clarify the role of this master playlist: Does it select one of the other playlists, and then select a song from that playlist? Or does it select the songs individually? This could be an important distinction. For instance, if one playlist (say, D) runs dry, and the master playlist in the first scenario picked D, you wouldn't get a song. But if it picks on a per-song basis, then if D is dry, then it just won't pick anything from D (since there's nothing there to pick). In this second situation, Punoqllads' answer would be correct, to within some minor edge effects and roundoff errors.

[ultrafilter]

What about a song rated two stars that has been played in the past seven days? We're assuming that it's not on any playlist, but I think that needs to be specified.

[Garfield226]

To clarify the role of this master playlist: Does it select one of the other playlists, and then select a song from that playlist? Or does it select the songs individually? This could be an important distinction. For instance, if one playlist (say, D) runs dry, and the master playlist in the first scenario picked D, you wouldn't get a song. But if it picks on a per-song basis, then if D is dry, then it just won't pick anything from D (since there's nothing there to pick). In this second situation, Punoqllads' answer would be correct, to within some minor edge effects and roundoff errors.

The second situation is correct.

What about a song rated two stars that has been played in the past seven days? We're assuming that it's not on any playlist, but I think that needs to be specified.A song rated two stars that has been played in the past seven days is not on any playlist.