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Trains of Thought

Computing with locomotives and box cars takes a one-track mind

Brian Hayes

All the Livelong Day

From the mathematical literature on railroad sorting, one might get the impression that putting the train in order is the end of all difficulties. The cars can then be dropped off at their destinations, one by one, without further thought. Train crews tell a different story. A memoir by Ralph E. Fisher, who worked on the Boston and Maine Railroad until the 1950s, refers to the process of making deliveries as a chess game. "Figuring out all these moves required no small skill if they were to be done in the shortest time and the least amount of motion."

Getting cars to their destinationsClick to Enlarge Image

Inspired by Fisher's stories, I offer the little puzzle (right). The task is simply to deliver cars 1, 2 and 3 to destinations A, B and C. The cars are already in delivery order. The procedure shown requires six reversals, three couplings and six uncouplings, for a total of 15 steps. Is there a better solution? Would some other initial permutation of the cars be more efficient? Is there a worse permutation?

The chess game of making freight-car deliveries is one aspect of railroading that has gotten easier in recent years. Many of the spur lines used for such local runs have been closed. Much rail freight is now shipped in containers or piggy-back trailers that are lifted off the train at a central terminal and delivered by truck. Such "intermodal" transport doubtless has several advantages. One of them is escape from the tyranny of the one-track mind.

© Brian Hayes

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