At time 0 a box contains one pen and one pencil. At each time n after, a item is chosen at random from the box and put back in together with one more item of the same type. (if a pen is drawn, then 2 pens go back into the box.) Let Xn denote the proportion of items at time n that are pens. We can prove that X_n is a Martingale, but show weather or not it converges.