We examine a Markov chain model for a random walk on the unit interval. That model is the subject of several problems, starting with 6.4.34, pp. 321 ff. in the book Marcel F. Neuts, "Algorithmic Probability: A Collection of Problems", Chapman and Hall, New York, New York, 1995. The random walk is studied by analytic, numerical and computer-experimental methods. Each of these approaches complement the others. Together, they offer an example of the diverse, hybrid methods that can be brought to bear on the contemporary problems of applied mathematics.