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?

I suggest that, in order better  to understand what this is all about,  we scale the problem down a bit.  Let us have but 2 spheres and be allowed only 3 drops. It then looks to me like we can't test higher than 4 meters. While there are exactly 7 3-bit binary numbers that have at most two 1's, I don't see how that necessarily gives a 7 meter testing range. Can anybody now give a straightforward explanation of what is happening in this scaled-down version?

Posted by Richard on 2006-05-05 23:50:38