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?

Try in order 0, 8, 16, 24, 32, 40 meters until there is a break or 40 is reached with no break.  Then use bisection to narrow down between where any break occurred and the next lower level. Three more balls could then break, exhausting the balls.  If the break was at 40 and three more tries are made, there will have been 8 tries total.  40 is thus a rigorous lower bound on the smallest height sought.

Posted by Richard on 2006-05-05 00:15:57