AN OBSTACLE-COURSE PROBLEM: I.

An obstacle course is presented in which n obstacles are given, together with the probability of successfully overcoming the ith obstacle. A runner is permitted to choose r or n r fixed obstacles and to order them, so that he maximizes his expected value, on the assumption that once he fails to overcome an obstacle he receives only the points previously earned. The optimal ordering of the chosen r is a simple function of the obstacle parameters. The optimal choice of which r to attempt is more complicated, and three alternative computational procedures are given, together with a proof that each will terminate at the optimal r, and an upper bound on the number of comparisons required for each. Author