I was asked this question (in essence) 4 years ago in the context of an undergraduate introductory astronomy course.

Given a spherical moon with radius r, and periodic impact craters formed on the surface of that moon with radius i every t years, what is the expected time elapsed for the entire surface of that moon to be completely covered with impact craters? Assume that the locations of impact are uniformly and independently distributed across the surface of the moon, at time 0 there are no impact craters on the surface, and the impacts will surely occur at times t, 2t, 3t, ...

Also assume i is smaller than r in order to be somewhat realistic; think of the size of the visible impact craters on our own Moon.

According to my TA the correct answer was the surface area of the moon divided by the area of the crater multiplied by t. Of course that is incorrect; only if there are no overlapping impacts will that answer be correct.

My TA wrote "unnecessary" on my assignment when I tried an unsuccessful probabilistic approach to solve the question as it was posed, and his lack of effort and dismissal of my effort was hurtful enough to make me remember the question from time to time ever since. However I sympathize with a busy and overworked TA.