You are studying the effects of gravity on clay spheres. You conjecture that they will shatter... but at what height? You want to find out the smallest integral height in meters from which the clay will fall and shatter.

Unfortunately, you only have four identical clay spheres, at least until the company that makes them starts returning your calls. Also, you only have enough time for 8 tests, during which the general area will be cleared of people. Last time someone did such an experiment, an egg... well, it was messy. Up to what height can you test the effects of gravity on the clay?

The question isn't asking you to find the height from which the sphere can be dropped without shattering.  The question is asking you what is the greatest height from which you can do your test, given that you have only 4 spheres and time enough for only 8 tests.  If you're looking for an integral height in meters, then you start at 1 meter.  Always assuming the best outcome, the sphere never shatters, and you have time for 8 tests, which takes you "up" to 8 meters.  If the sphere breaks before that, you've got the answer to your test.  If it doesn't, you come back tomorrow and start dropping from a height of 9 meters.

 

The answer?  8 meters

Posted by Tristan on 2006-05-09 16:20:34