What are some assignments that you given to PMM candidates during the interview process?

Common assignments we've asked candidates include: 

• How would you announce a new feature? (How would you approach developing messaging for this launch? Suggest 3 tactics you would employ to announce this feature to customers. Who are the internal stakeholders you would work with, and in what capacity? How would you think about measuring the success of this announcement?)
• Provide a high-level strategy for how you'd tackle competitive research 
• Give a 1-2 sentence (original) pitch on our product 
• How would you go about understanding the personas we should target with a new product?
• How would you ensure the sales and marketing teams understand the target audience and messaging? What type of activities or deliverables would you create?

None

I know sometimes this answer is controversial, but there is such a power imbalance as an interviewer that I think it is incredibly unfair to ask all of these people to each put in the time, on their own, to do essentially a PMM activity for free. If you're a PMM who knows your craft and is interviewing someone for a role, you can instantly tell someone's skill level and experience. There is enough about this job that can be so complex that most of us advanced in our careers have seen it all and can talk through various levels of experience with it. In my experience, the interviewers who require assignments struggle with the PMM craft themself. 

And for someone new in the career, without experience, case questions are wonderful (hypothetical questions that give you insight into how the candidate thinks). 

All-in-all... I'll take a collaborative, motivated, excited learner who wants to come in and make stuff happen over an experienced PMM any day. I can teach and mentor the skills of PMM without a second thought, its much harder to teach culture and collaboration.