Finding direction of rotation
Posted on 2011-03-08
There is a disk on a turn table. Half of it is black, and the other half is white. It is rotating in constant speed, but it's rotating fast so that you can't see whether it's going clockwise or counterclockwise. You also have a set of stationary sensors you can install anywhere which can tell whether the color of a spot has changed from black to white, or vice versa. What is the minimum number of sensors needed to find out which way the disk is rotating? What is the best, average, worst time to figure out the direction? If you use more sensors, can you improve the best, average, worst time? How can you accomplish that? If you are given only one sensor, how can you find out the direction, assuming you can change one constraint of the problem?