An Open-Ended Question on the PRIMES Entrance Test

I am the head mentor of PRIMES. From time to time one of our mentors tells me that their project is stuck. I then meet with the mentor and their student to brainstorm possible alternative directions. When students suggest their own direction they are more passionate about it and the project gets unstuck. Sometimes a new direction points away from the original question. But after resolving the new problem, the students gain insights and techniques which help them to successfully come back to the original project. In any case inventing a question is an important part of research. So this year I suggested including a similar brainstorming exercise in the entrance test: