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?

(In reply to Question by Salil)

The 7 refers to a possible answer to the problem, that is, the height to which one can test.  What rules out 7 in the scaled-down version?  There are 7 ways to perform 3 tests and shatter no more than 2 spheres, so why are there not 7 sets of 3 heights that are usable for testing and which will test all whole-number heights 1 through 7?

Posted by Richard on 2006-05-07 12:17:24