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 re(2): Possibly right solution, partial expl. by John)

Um, I'm not sure what you're asking, because I think you answered your own question:

"let's say it was 13:  12 > 18 (break) > 15 (break) > 13 (break) so that's 4 breaks and you haven't tested 14m yet."

I'm not exactly sure what's going on there, but if it broke at 13, you wouldn't have to test 14...  and you said "let's say it was 13", and then you found it to break at 13, which is the idea.  For example:

1st - 24 - break

2nd - 12 - break

3rd - 18 - break

At this point you have 1 sphere left and 5 trials remaining, so you can test, in order, 13, 14, 15, 16, and 17. 

Posted by tomarken on 2006-05-04 15:14:09