Should a teacher be able to solve all the assignments they give their students themselves? A moment ago, I happened upon https://puzzling.stackexchange.com/questions/99712/almost-impossible-sudoku-like-puzzle which explicitly mentioned that this student was given a puzzle in math class that his math teachers couldn't solve. And it got me thinking: To me, it feels like a teacher like that is unfit for teaching. After all, how could they impart knowledge they don't have onto their students?
Should a teacher be able to solve all the assignments they give their students themselves? Assuming the assignment is in fact solvable obviously.
Note: The question that prompted this was a math problem, but I'm looking for course-agnostic answers, if possible.
In general, yes, a teacher should know how to do any assignment and, in some cases, should have actually done it. In teaching programming, for example, it is usually a mistake to assign a problem that the instructor hasn't essentially done themselves.
The reason is that one of the tasks in making assignments is to estimate the effort and time required to do the task. If you can't solve the assignment yourself, you are giving an open ended task to students. In almost all situations students have a limited time to spend on any given assignment and that competes with their other tasks.
There is an exception to the above. If you tell the students at the beginning that you are assigning something you don't have an answer to, and will be grading their efforts rather than their results, then you can make this work. The assignment becomes an exploration. At lower levels of education this makes less sense than it does at higher (say, doctoral) where it is natural to explore the unknown.