For me the centerpiece of a design exercise is seeking knowledge and adapting your design ideas to that knowledge. You create and adapt and discard ideas readily and easily if they don’t fit the emerging situation. So it is essential to ask questions during the exercise to understand as much as you possibly can about the people, environment, stakeholders, goals, and constraints so that you can demonstrate this process.
You don’t want the entire exercise to be taken up with this “research” activity – you do need to design something. So consider offering a very rough concept and then asking questions that will lead you either deeper into or away from that concept.
Example – imagine Home Depot had a magical way of printing and delivering orange aprons to new employees, and employee apron customization/self-expression is culturally important. What ideas does this spark? What do you want to know to confirm or discard some of these ideas?
My thoughts immediately go to a part of the new employee offer process that leads people to a website where they can customize an apron at their leisure. But these are hourly employees – the store manager is not going to want ANY work activity to be done outside of the store or in off hours. So the kernel of that idea needs to come in-store. Come to find out that they’d also like to offer this capability to existing employees. What is the technical environment in-store? How much time is the store manager willing to have an employee spend on this while on the clock? What are the required elements of apron customization and what are the optional ones? Etc. Understanding these you can sketch out a process that quickly gets the basics taken care of (perhaps in ONE or ZERO steps) and offers any options easily and quickly.
In a design exercise you’d do this all narratively – talk about the core idea, check it against their answers to your questions, change the core idea, sketch a little, ask more questions, adapt to the answers, etc.