Today at my virtual talk at the Scholar Search Education Forum at Northwestern, a student asked me about the hardest math problem I’ve solved. I thought of the hardest problem I haven’t solved. I love it because it came from a real situation!

Say there are 36 people at a workshop. They get in groups of 6 and work for a while. Then, they regroup into new groups, so no one is in a group with anyone they’ve been with before. How many times can they regroup before someone has to be in a group with someone they’ve worked with before?

I also wonder, how could you extend this problem? If you’ve answered the specific problem, what else does it make you wonder?