Faculty Sponsor

Dr. James Caristi


Arts and Sciences


Department of Mathematics and Computer Science

ORCID Identifier(s)

0000-0002-3829-0053, 0000-0002-6258-1766

Presentation Type

Poster Presentation

Symposium Date

Summer 7-28-2015


This research project sought to find general track formations that allowed battery operated locomotives to traverse the entire train track in both directions infinitely. These formations allowed for any number of track pieces from TrackMaster Thomas and Friends sets by Fisher Price. The research looked at start position of the train and presetting of the switches as well as what is necessary to have a complete track with no dead ends. Surprisingly, there was found to be only one track formation that allowed for entire traversal of the track in both directions. This layout was termed a "dog bone" and consisted of two switch pieces connected at the ends with the tips of both switches connecting to themselves on the same switch. A proof that this layout is the only layout that satisfies the conditions is given.

Biographical Information about Author(s)

The authors are both Mathematics and Secondary Education majors. They found the topic interesting because it reminded them of their childhoods. The question was stimulating and there have been several other interesting find while working on this project. They have both enjoyed working on this, their first, research project.