Data Science Take Home Challenge Interpretation of Question I am currently applying for a Data Science position and have to finish a take-home challenge for one of the companies. However, I don't really understand what they want me to do and hope you can help me interpret the question. Unfortunately, I can't reach anyone at the company due to Christmas holidays

I have a data set with transactions of customers and another dataset with information about age, country... of those customers. Now I am asked to define a target metric for engagement and say how I would define unengaged vs. engaged customer. Afterwards, I have to use this logic to build a model to classify engaged vs unengaged customers (they point out overfitting due to feature used in the target metric).

How would you interpret these questions?

Do I first have to say if target_metric > x: engaged and then build a supervised model to classify the users again?

OR

Would you define several metrics that could separate engaged and unengaged customers and then use an unsupervised model to find two clusters that would then be engaged vs unengaged?

I tried to keep the question as general as possible to avoid "cheating". I only want to know how you would interpret them. Thanks!
Second one but dont stop there.

First of all you specifying if target_metric > x: engaged is just wrong and you have to let data tell you this x, not you choosing it.
Second one seems nice I would start with that, do some extensive analysis and only then start finding x empirically. How? just of the bat you can pose it as minimization problem for different x and find the one that has biggest purity/separation between classes.

Why dont stop there? There is no wright and wrong, if you have some plausible approach in theory but it fails in practice I would definitely
include it and elaborate on it, discuss it etc...