NP: If transition probabilities are uniform over all trees, how is the rate at which bug populations on individual trees change related to the values in the S’’ and/or S’ sequence, where S is the sequence of populations?

NP: How are the S, S’ and S’’ sequences related to the numbers on a complete Trapezoidal Approximation Graph?

NP: How can the changing temperature of an object in a room be modeled as a bug diffusion problem? How do we model this situation as a random walk?

NP: Given the rate-of-change laws that govern the exit of a gas from a container, predict the pressure vs. clock time for the air in a bottle rocket as it expels the water inside. Reward for solution: satisfaction and the right to shoot some bottle rockets.

NP: How could we shape a container so that the water level would change at a constant rate? How would we design it to that the rate of depth change would be proportional to depth?

NP: Using matrix calculations or Excel column operations test whether when we start with a large number of trees with the population 'spiked' in the middle, the population distribution random-walks through a series of normal population distributions with increasing standard deviation. Does the standard deviation change at a constant, a decreasing or an increasing rate?