A Grecian urn contains 75 white beans and 150 black beans. Next to the urn is a pile of 200 black beans. Pick two beans at random from the urn. If at least one of the beans is black, place it on the pile and drop the other bean, whether white or black, back into the urn. If both beans are white, discard both white beans, pick a black bean from the pile and drop it into the urn. Question: Will there ever be just one bean in the urn and if, so, what will be its color? Click on the green flag to find out.
This problem appeared in A.K. Dewdney's Mathematical Recreations column, March 1991, Scientific American. The problem originated with Ross Honsberger, University of Waterloo, Canada. Not having a Grecian urn and an assortment of white and black beans handy, I decided to write a Scratch simulation. This problem illustrates the curious fact that even though the process of drawing the beans is random, the outcome is purely deterministic! Questions: 1. What is the outcome, every time? 2. Does the program always terminate at the same Draw#?
