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.