Finding the Median under IOI Conditions

We explain the ingredients of the International Olympiad in Informatics (IOI), which is a challenging competition for high-school students focusing on algorithmic problem solving. We treat in detail the \textsc{Median} task, which the authors created for IOI~2000: Given an odd number of objects, all of distinct strength, develop an efficient algorithm to determine the object of median strength, \emph{using as \emph{only\/} operation a function that returns the median of \emph{three\/} objects}. This problem is easy to formulate and understand. It is related to well-studied standard computing problems, but further analysis of this problem leads to interesting algorithms and variations of the heap data structure. We finish by pointing out some open problems related to this task and we invite you to contribute nice competition tasks for future IOIs.