Observations of sea ice displacement over short periods of time are used to deduce some statistics of the ice motion over long periods of time. The objective is to follow the trajectory of a piece of ice, starting at a randomly selected time and location and ending when the ice either melts or leaves the Arctic Basin. Trajectories are also followed backward in time to the time and location where the piece of ice was formed. Statistical properties considered are the age and remaining lifetime of ice in various locations and the probability that ice presently occuplying a particular location was originally created or will ultimately melt in certain regions. Possible applications are to the distribution of pollutants by sea ice and to the design of experiments involving drifting measurement platforms.