My favourite version of this problem involves 4 eggs and a 10^6 floor space elevator. It's small enough to figure out on a whiteboard, but large enough that you can't do it without figuring out the pattern.
The cat can survive a fall out of a low story window, but will die if thrown from a high floor.
This is a faulty postulate that cannot be overcome by even the most rigorous math in the world.
Although controlled studies have not been done (fortunately!), case statistics assembled by New York City veterinarians suggest that in many cases, falls from higher floors may actually be more survivable. One theory is that cats have more time to right themselves before reaching terminal velocity.
Of course, the problem with the question is that the OP chose cats, as if it's humerous to think of throwing a cat out of a high window. The problem at its core is the relationship between height, accelleration, and materials. What is the necessary height for a given material to reach a sufficient velocity to cause it to fail upon impacting the ground?
I realize that using eggs instead of cats probably would have been more applicable to this problem. But OP inadvertently demonstrated another problem: proofs built upon flawed postulates are not only flawed themselves, but a colossal waste of time. I wonder how many scientists and engineers in the real world are spending so much time calculating the trees that they've lost sight of the forest. Probably more than most people think.
I came here to post the same thing, after hearing about these studies on Radiolab's recent episode on falling. If I remember correctly, another theory that they discussed was that after the cat reaches terminal velocity it relaxes its body since it is no longer distressed from the acceleration.
That episode was another great one, I think the whole show is something a lot of HN readers would enjoy. Here's the link to that segment:
Is it not also possible that cats that fall from higher floors are in fact much more likely to die immediately and thus never see a veterinarian and never get included in their statistics. That would suggest that the injuries tend to cluster more round the extremes at higher floors but even then there could be alternative explanations.
This, of course, is a popular interview question, albeit asked with eggs (or bowling balls) instead of cats. Here's a discussion and a solution: http://20bits.com/articles/interview-questions-two-bowling-b.... I think for m balls and N floors, the number of steps is O(N^(1/m)).
I'm not sure if it's interesting, funny, or sad, that almost all of the responses were talking about the cats, and how they do better with higher falls, and almost none talked about the actual question.
Problems like these are good for new programmers to think while keeping abstract thought farther away.
Using cats rather than eggs or dogs paints a story that's fun to imagine. I could also ask the question by saying: there is an integer to find and any integer guessed above this removes one chance
I wonder how people might go about constructing their answer if they worry with respect to the cats lives as compared to the abstract version
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[ 6.9 ms ] story [ 13.8 ms ] threadThis is a faulty postulate that cannot be overcome by even the most rigorous math in the world.
Although controlled studies have not been done (fortunately!), case statistics assembled by New York City veterinarians suggest that in many cases, falls from higher floors may actually be more survivable. One theory is that cats have more time to right themselves before reaching terminal velocity.
http://www.pets.ca/cats/articles/cat-jumps-off-building/
That episode was another great one, I think the whole show is something a lot of HN readers would enjoy. Here's the link to that segment:
http://www.radiolab.org/2010/sep/20/taking-plunge/
Almost right. It's O(m N^(1/m)).
Using cats rather than eggs or dogs paints a story that's fun to imagine. I could also ask the question by saying: there is an integer to find and any integer guessed above this removes one chance
I wonder how people might go about constructing their answer if they worry with respect to the cats lives as compared to the abstract version