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 Detailed Solution by Salil)

You're right,

I knew there was something fishy about my result. I have since edited my solutions (I had skipped 111 for anyone keeping track).  There are 163 unique outcomes for the answer to the question "What is the maximum integral drop height for which the pot will survive?" including zero meters and "at least 162 meters".

For the question of "What is the minimum integral drop height for which the pot will shatter?" we are sort of assuming that zero meters is not a shatterable height so we can give difinitive results through 162 meters but should the eighth drop from 162 not shatter we can produce no answer but "some height greater than 162 meters".

Posted by Eric on 2006-05-05 22:03:27