You are given a 100*50 snooker table (felt area) and two balls of diameter 1. One ball is placed in the center of the table and the other ball is randomly positioned. What is the probability that I will be able to shoot this second ball directly into the top left pocket without touching the central ball? (Assume pocket has radius 1)
I thought this was a great problem, but I am perplexed at how the pockets work. Does the table have 6 pockets in the normal places? Are the centers of the radiussed pockets directly on the edges of the rails? Are the rails perpendicular to the table (remember that rails do not normally touch balls on their great circles)? At each pocket, is a circular arc extended out into the table, thereby defining the pocket and reducing the area where a ball can be randomly placed?
It might be reasonable to assume that the table is like an infiite plane with a 50 by 100 fence installed with an open gate in the one corner angled at 45 degrees with width squareroot of 2. Not quite like a snooker table but it is at least well defined.
Can anybody give an exect answer without approximation?

Posted by bernie
on 20060216 14:59:56 