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?

This is my solution. I do not know if I missed anything. The max height would be 241 m. 

The first list of heights  are 91, 153, 193, 217, 230, 236, 239, 241

The second list of heights are ( 29, 51, 67, 78, 85, 88, 89), (113, 129, 140, 147, 150, 151), (169, 180, 187, 190, 191), ( 204, 211, 214, 215), ( 224, 227, 228), ( 233, 234 ), (237)

The Third list of heights are ( (7, 13, 18, 22, 25, 27), (35, 40, 44, 47, 49 ), ( 56, 60, 63, 65 ), (71, 74, 76), (81, 83), (86)), ((97, 102, 106, 109, 111), (118, 122, 125, 127), (133, 136, 138), (143, 145 ), (148)), (158, 162, 165, 167), (173, 176, 178), (183, 185), (188)), ((197, 200, 202), (207, 209), (212)), ((220, 222), (225)), (231)

The fourth list of heights are (((1, 2, 3, 4, 5), ( 8, 9, 10, 11), ( 14, 15, 16), (19, 20), (23)), (( 30, 31, 32, 33), (36, 37, 38), (41, 42), (45)), ((52, 53, 54), (57,58), (61)), ((68, 69), (72)), (79))), (((92,93,94,95), (98, 99,100),(103,104), (107)), ((114, 115, 116), (119, 120), (123)), ((130,31),(134)), (141))), (((154, 155, 156), (159, 160),(163)),( (170, 171),(174))), ((181))), (((194,195), (198)), ((205))), (((218)))

 

Edited on May 5, 2006, 1:22 pm

Posted by Salil on 2006-05-05 13:20:25