How about a problem to design a multiplexed moving led-matrix display? Offer the capacitor discharge method as a "hint", but make the display large enough that a basic approach will only barely work.
and get a million posts "I expanded it, why does it not work"

It doesn't have to be an outdoor type, which taxes the available technology in a number of ways
That does not "tax the available technology" it does tax some technologies, but not available technology, if, indeed it does, I will request a huge raise.

it does have to be properly timed, properly multiplexed, properly adjusted for brightness, and, in the event the designer wishes, it has to have the proper time constant in the capacitor's charge path and discharge path to allow the LED to attain proper brightness, yet allow for long-term survival of the LED's and NPN's.
look at how many times you used 'properly' that should say something.

Since it does require study and comprehension of datasheets, and how various parameters interact, as well as some understanding of retinal persistence and LED behavior, and how they interact, a thorough and complete treatment of the problem should earn any student a better-than-just-passing grade.
been there, done that and, it's a bitch. The one thing that is so often overlooked with multiplexed "feature rich" displays is the "time globs". "time globs" is, in some cases, not a problem, but in others it will lead to total project failure.

The problem probably will turn out to be quite straightforward for serious engineers in a serious engineering curriculum, yet still comprehensible to students in a technical course more focused on practical implementation than on theory.
I can design such a display in minutes, but ONLY if a "briefly dark display when certain things happen" is allowed. Some of this can be overcome, but the complexity of the design will expand exponentially. Were I to make s dot matric display for an alarm clock, I would likely multiplex, but that is about the limit.

Since there are MANY variables, it will turn out to be more of a "linear programming" (optimization) type of problem than a math problem with only one discrete solution, and will challenge nearly anyone at that level.

you are right there, I would expand to any level.

The 'problem' with multiplexing is that, while it, in many cases, is an excellent solution for small displays, it does not lend itself easily to larger displays.

Erik