Hi there,
This is a very very common problem! I see it all the time.
Ultimately, expect to see the unexpected. In all aspects of your interview (and your future job), take on a mindset of: "I will not expect what is coming. I will adapt continuously based on new information as it comes through"
Here are some tips for you.
How to better brainstorm when stuck
- Practice/Prepare - The more you practice cases, read case studies and articles (The Economist, The FT, etc), the more "example" you'll have, as you just have more base knowledge to work with.
- Repivot and Frame - Pause. And look at the ideas you've come up with. Talk to the interview with you frame/group them. This 1) Shows them you can organise your thoughts 2) Helps you gain some time AND identify potential holes yourself 3) Gives them a window to point you in the right direction (they might say "Ok, that's a good bucket, but it's missing something" or " You're missing a bucket that relates to what you';ve said here")
- Ask for Help - This is a tricky one to navigate, but you can ask questions or make statements that try to glean more information from them. For example, "I'm out of ideas, but have any competitors excelled in any areas"..."Do we have any analysis on this?"..."etc. etc.
How to "Ask for Help" or "Buy Time" When Stuck
1) State that you're now figuring out where to take this next (that's fine)
2) Recap the objective and the pieces of information you need (and have) to answer the question/hypothesis.
a) Hopefully this triggers something or b) You get a signal from the interviewer on a particular segment (they might probe you and say "is that all we need from bucket x?"
2) If this doesn't work, start to probe in different areas (i.e. do we know x? To double-check you already said y doesn't apply, correct?) etc. etc.
3) If really desperate, you can say something like "Has the client experienced this before or have any ideas they've come up with?" or "Have we observed something similar to this problem in the past that we can leverage?"
How to Ask Good Questions When Stuck
You need to picture yourself at the client site, in front of a whiteboard, with your team, figuring out what you need to do next on this project.
Truly reflect on what you need, what you're missing, or what you don't currently understand about the situation. Then, ask questions to fill this in.
This is super hard to learn, and impossible to teach through some written tips/techniques. I'd be happy to give you a crash course in this - 1 hour is all you need to have a complete mindset shift in this area!