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: Question by Richard)

You have to count zero meters.

Let 1s indicate breaks and 0s indicate bounces (or thuds)

110 refers to the first two pots breaking at heights of 3 and 1 meters so the maximum integral survival height is zero meters. This ranges to 000 which refers to surviving drops at 3, 5, and 6 meters. This means the maximum integral survival height is six meters or more. Here are all seven binary combiniations given in maximum integral survival height:

110 -> 0
101 -> 1
100 -> 2
011 -> 3
010 -> 4
001 -> 5
000 -> 6 or more

Posted by Eric on 2006-05-08 16:22:01