>An event in Dantzig's life became the origin of a famous story in 1939, while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.[4][7]
>Six weeks later, Dantzig received a visit from an excited professor Neyman, who was eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics
i audited university of Chicago's undergrad "hard-track" real analysis (i forget the name, but iirc there was an easier version of the course available).
The problem sets would have several questions you were expected to solve, and then often 1-3 questions marked with 1 or 2 stars. I forget exactly the language, but there was some explanation that you probably couldn't solve the 1-star problems, and solving the two-star questions could be someone's PhD thesis, as it would require novel insight into an unsolved problem.
The point was that it was a class for young aspiring mathematicians many of whom were used to being the smartest person around, and this helped them confront problems they couldn't solve without feeling like total failures. Also at that kind of school, you never know, someone might be able to solve one.
Not quite the same, but David Huffman was given a choice between writing a term paper on finding the optimal binary code and a final exam. Just before he was about to give up on the term paper, he solved the term paper problem by inventing Huffman Coding[1].
my own huffman story: I took huffman's class, cybernetics, in college (thinking that it would teach me how to build robots that interfaced with humans). However, the class was mostly about how to build circuits, and Karnaugh maps weighed heavily. The final problem on the final test was a tricky Karnaugh map and I got it wrong- although I knew that you could form squares that "wrapped" around the top and bottom edges, but he put a square that was wrapped around the four corners:
1 0 0 1
0 0 0 0
0 0 0 0
1 0 0 1
and I totally missed that the symmetry applied in both directions at the same time (I'd call that a tricky question rather than a trick question).
That class led to a ton of imposter syndrome that took me decades to overcome. Thanks, Huffman.
A teacher of mine, who studied maths at Oxford, was given a problem sheet on his first day and was told to finish by the time of his first tutorial. He made no progress and was reduced to tears as he thought he was incapable at Oxford. Turns out, he was given a set of unsolved problems on purpose :)
>An event in Dantzig's life became the origin of a famous story in 1939, while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.[4][7]
>Six weeks later, Dantzig received a visit from an excited professor Neyman, who was eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics
https://en.wikipedia.org/wiki/George_Dantzig