True story: In a tough astronomy Oral Exam, my grinning professors posed this problem:
"How would you determine the density of Jupiter using only a pair of binoculars? Assume you don't know the planet's distance."
"Umm..." But, to my surprise, I figured it out.

Once outside the exam room, I boasted of my accomplishment to my friend Rico. "Impossible!" he proclaimed. I bet him 10$ and won. How did I do it?