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 Possibly right solution, partial expl. by Jer)

But if 7 is a break, and you test 1 through 5, you don't know whether or not it would break at 6. 

I came up with an initial solution of 87 feet being the highest we could potentially test.  Perhaps the difference in our solutions hinges on the fact that you made the assumption about the 6th sphere at every step.

The first drops I came up with (until one breaks) were 24, 44, 60, 72, 80, 84, 86, and finally 87.  If, at any point in that sequence, a sphere breaks, there will still be enough spheres and trials left to find the exact height at which it breaks.

Posted by tomarken on 2006-05-04 14:17:26