Consider a 380 story-building. Your task is to determine the highest floor, one can drop a pumpkin from, without smashing it. To answer the question, you have four identical pumpkins at your disposal, which you may use for test droppings. Obviously, once a pumpkin got crushed, it is no longer good for testing.
We make the assumption that, whether those gourds break or not, depends entirely on the height from which they fall. In particular, it does not matter how many previous descents the vegetable endured, as long as it is still intact. However, since this is not a physics or botanics problem, we cannot make any assumptions as to the toughness of those culinary fruits ;)
What is the minimum number of droppings needed to identify the crush-critical height?
From which floor should you throw your first squash vegetable?
Note: See Egg drop for a similar, but slightly easier challenge.
OK - but I am not a snob, but rather a bit of an idiot, and so I take this one on.
Pumpkins smash, transferring their potential energy (m h g) into kinetic energy in transit (1/2 m v^2) at about 5-15 feet, which ls less than one story of a building. On impact, the energy dissipates into friction and distortional energy. If the distortional energy is sufficiently large in this inelastic collision, the pumpkin breaks apart.
The problem asks about at 380 story building... Oh my! The most stories of any building to date has is the Burj Khalifa at 163.
Anyway - unaided, a pumpkin survives less than a one story drop, so I would drop the four successively from higher and higher windows (recycling the un-smashed pumpkins) until the absolute smashing height was proven with repetition. I would imagine 6 or 7 drops would prove the height and leave all four pumpkins smashed.
Edited on February 1, 2020, 3:23 pm
a fairly idiotic problem
