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?

I got 247 feet - I hope I did all the adding right.

I'm also not sure yet if you can do a little better if at some point you have more spheres than you have drops left.

The first drops (until one breaks) are at 92, 155, 196, 221, 235, 242, 245 and 247 feet.

If 92 is a break, the next drops are 29, 51, 67, 78, 85, 89, 90
If 29 is a break, the next drops are 7, 13, 18, 22, 25, 27
If 7 is a break, you only have 1 sphere left, so drop the final drops are 1, 2, 3, 4, 5 (If 5 is not the break 6 would be)

Posted by Jer on 2006-05-04 14:09:26