If your first paragraph was actually in the question then I would agree, but in the actual question, the reason there are exactly 100 people in line is that the question says there are 100 people in line. Phrasing certain parameters in your question as though they are absolutes and then expecting the person answering the question to change those parameters is like the worst kind of trick question. It's like when a toddler asks you if a ninja or a pirate would win in a fight, then says the pirate would win because he secretly has super strength. It's cute when a toddler does it because they innocently don't understand why their question wouldn't logically convey that hidden parameter to the listener, but inexcusable for a professor.

Getting the ability to reason about this question is why people take the course.

It's the same with software engineering, being able to reason about possible bugs just by looking at some code comes from training/experience.

Now, on this problem, some train of thought is like this:

100 people join of their own free will, no limit other then value-from-waiting > value-from-not-waiting.

If extra coffeee then valueFromWaiting - valueFromNot = 75c. Cost per person 0.25c

But... this means more people queue up ontil valueFromWaiting - valueFromNot = 0. (basic economy knowlege being tested)

So what's the grand cost and how come it's 100$?, well, I could argue that

Sum(1$ - valueForPerson(i)) from 1 to NewEquilibriumPersonCount == Sum(1$) from 1 to OldPersonCount.

Because NewEquilibriumPersonCount is function of ValuePerPerson. (can probably deduce how given some time or some reading would help)

Grasping this sort of logic is when GPT will be scary.

I think you're just reading an ambiguous sentence in a way that obviously wouldn't make sense in context. The question is in a very familiar form: describe a scenario with some assumptions, describe a peturbation, ask what impact the peturbation has. If the context was some annoying internet quiz, the answer might have been a gotcha that the number of people in the queue stay the same.... but this is an econ question it's going to involve how people respond to economic incentives.

This is like those LeetCode questions in job interviews, or the interviewer wants a complicated O(n) solution when the problem as stated would be better solved with a simple O(n^2) solution because the maximum problem size is tiny.

It's a mind-reading game of which assumptions the professor/interviewer wants to keep solid which ones are open to change.

Instructions weren't clear, ended up with a free cafe in front of raspberry store.