Sure but that's a solution to prevent students from using LLMs, not an example of something a professor can ask students that "LLMs can't do"...

The main challenge is that most (all?) types of submissions can be created with LLMs and multi-model solutions.

Written tasks are obvious, writing a paper, essay or answering questions is part of most LLMs advertised use-cases. The only other thing was recorded videos, effectively recorded presentations, thanks to video/audio/image generation that probably can be forged too.

So the simple solution to choose something that an "LLM can't do" is to choose something were an LLM can't be applied. So we move away from a digital solution to meatspace.

Assuming that the goal is to test your knowledge/understanding of a topic, it's the same with any other assistive technology. For example, if an examiner doesn't want you[1] to use a calculator to solve a certain equation, they could try to create an artificially hard problem or just exclude the calculator from the allowed tools. The first is vulnerable to more advanced technology (more compute etc.) the latter just takes the calculator out of the equation (pun intended).

[1]: Because it would relieve you of understanding how to evaluate the equation.