129 - ZOJ Monthly, December 2013 - H
Aha is suffering from terminal illness while a fatal disease is attacking one of his organs. After modeling the organ with lesions, we believe that the organ is a circular slice. More unfortunately, the annual advent of a fatal lesion point on his organ sounds the death knell for Aha, and the fatal lesion point falls on the surface of the existing sick organ equiprobably. Every year he turn to a doctor who will preserve the maximal circular portion of the organ without the lesion point and excise the rest part during the yearly surgical operation. Once the area of the Aha's sick organ is less than 25% of a normal organ, he has to enter the grave desperately.
Now we have measured the area of Aha's sick organ in a minimally invasive vivisection experiment. Then what's the expectation of his rest time?
One line per case, indicates the area of Aha's sick organ, in percentage of the area of a normal organ.
A one line per case, indicates the expectation of Aha's rest life in years. And the absolute error should be less than 10-8.
When the area of Aha's organ is equal to 100% of a normal organ, he can live about 4.39 years in average.
Author: ZHOU, Yuchen