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: That's the breaks (Possible correct solution) by tomarken)

You are right again, tomarken.  I saw my error just after I posted, but had no time to change it.

Here is a revised answer.

Drop the first at a height of 64 meters. If it doesn't shatter, continue with the following: 106, 132, 148, 156, 160, 162,163.

If it shattered on the first drop, then drop it at 22 meters.  If it doesn't shatter, continue with the following: 38, 49, 56, 60, 62, 63.

If it shattered on the second drop, then drop it at 6 meters. If it doesn't shatter, continue with the following: 11, 15, 18, 20 and then 21.

If it shatters on the third drop at 6 meters, drop it from 1 meter.  If it doesn't shatter, continue with the following: 1, 2, 3, 4, 5. 

A height of 163 meters can be reached.

Eric gives a good diagam of the solution in the following post.

Edited on May 5, 2006, 4:29 am

Posted by Dej Mar on 2006-05-05 02:20:38