Assigning Open Problems in Class

I had an advanced algorithms professor who was brilliant but not always put together. Eg - he didn't always dress himself correctly. Think, two different shoes or a button shirt mis-buttoned so there was an extra hole at the top.

He came in one day and wrote this problem on the board, and asked if anyone could solve it in O(n log n). No one did, he seemed really disappointed. The TA came in afterwards, and someone asked why we were going over this specific problem. Would it be on the final? The TA said "You professor gave you this problem because he went to a conference recently, and this was announced to great fanfare as a new unsolved problem. For the last two weeks, he's been asking anyone who will listen if they can solve this problem."

My dad told me a story about his college days; Professor gave everyone a problem to work on over the weekend. He went home and spent hours on it, but couldn't figure it out. Came back to class Monday and everyone else had issues with it as well. Professor walks in: "Sorry everyone, that problem was actually unsolvable."

This reminds me of my undergrad “discrete math” lecture notes, where my professor wrote the following in the unit on sets:

> This brings us to a fun problem for you to think about in your spare time: are there any infinite sets that have cardinality strictly between [the cardinality of the natural numbers] and [the cardinality of the real numbers]?

This is of course the famously undecidable continuum hypothesis (https://en.wikipedia.org/wiki/Continuum_hypothesis).

I mean, why not?

Haven't people seen the documentary, "Good Will Hunting"?