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?

My first thinking was to consider what could be tested if the first three tests fail. Then I'd have up to five attempts to test the last sphere beginning with 1 meter through 5 meters. This implies that if the first two tests fail, the third test should test 6 meters. Should that succeed we can then test up to 11 next and still cover 7 through 10 should it break. I think the extension of this logic will produce our desired result.

Posted by Eric on 2006-05-04 12:53:36