Question

I had that feeling of getting more than you ought to a couple of weeks ago when reading the first chapter of Rota and Klain's Introduction to Geometric Probability. In particular, I was familiar with the usual derivation of the probability of Buffon's needle crossing a line. So it was amazing to read the solution to a harder problem, Buffon's noodle, which is solved by appealing to a much simpler seeming general symmetry argument. And like you describe, it forms a kind of teaser trailer to draw you you into the rest of the subject.