These threads are often fun because of the variety of ways people were taught things. It’s hard to guess how they compare because most people only end up doing one of the ways and there isn’t much randomisation in education.
Where I studied, problem sets were purely pedagogical and didn’t contribute towards grades. It meant exams could be stressful but the questions in the homework could cover a wider range of difficulty including things that would be fun to have a crack at even if you didn’t know the answer. The struggle of trying to figure it out felt good for understanding the material. We’d review answers and solutions in small groups after attempting the homework. It was pretty normal to get prove-or-disprove or could-one-prove questions but this was mathematics not economics.
A few problems I remember in particular:
- in an introductory course a few weeks in there was a question like ‘find a function R -> R that takes every value on every non empty open interval’ and there’s a standard construction that we didn’t generally know so there were often fun errors or weird constructions.
- ‘find a space X which deformation-retracts to the annulus and to the mobius band’ which I mostly remember because I had some horrid intuitive solution where I took a disk times a circle, embedded it in R3, and then carefully wrote out retracts, but I think the good solution was to just take the product space and then rely on some theorems that I no longer remember
- ‘what’s yellow and equivalent to the axiom of choice?’