Streaming services often use artificial intelligence to recommend music. One way to do this is to represent song attributes and a listener’s preferences using numbers or points on a grid. Recommendations for a listener can then be made by looking for songs represented by points that are close in distance to the point representing the listener’s preferences.
A particular music app represents song attributes and listener preferences using two scores: Energy and Happiness, which are each integers from \(1\) to \(10\). Suppose that three songs are represented by the following points:
| Song | (Energy, Happiness) |
|---|---|
| \(A\) | \((5,5)\) |
| \(B\) | \((4,3)\) |
| \(C\) | \((2,8)\) |
Plot each song as a point on a coordinate grid. Denise’s score is represented as \((6,4)\). What song do you think the music app will recommend to Denise? Why?
Philip’s score is \((3, 9)\). Determine the Energy and Happiness scores for a song that both Denise and Philip might enjoy. Explain your reasoning.
After an app update, a song is recommended if both its Energy and Happiness scores differ from the listener’s scores by at most \(2\). How many different scores of \((E,H)\) could there be in the songs recommended to Denise?
Theme: Computational Thinking