Ideas about graph theory and, in particular, about things called “Hamiltonian paths” are helpful in solving this problem. (See Extensions for a short description of Hamiltonian paths.)

Online resources on graph theory include:

• "The Mathematics of Graphs and their Games" at http://www.cs.uidaho.edu/~casey931/mega-math/workbk/graph/grbkgd.html. This site provides a thorough and accessible introduction to the ideas and terminology of graph theory as well as classroom lesson plans for elementary students on up.

• "Graphs" at http://www.cut-the-knot.com/do_you_know/graphs.html. This site discusses introductory graph theory ideas and provides an interactive graph-making tool.

Almost any book on graph theory, including many “discrete math” texts, will talk about Hamiltonian paths in a graph. Here are a few suggestions:

• Bondy, J. A. and Murty, U. S. R. (1996). Graph Theory with Applications. New York: Elsevier Science Publishers.

• Goodaire, E. G. and Parmenter, M. M. (1998). Discrete Mathematics with Graph Theory. New Jersey: Prentice Hall.

• Merris, R. (2001). Graph Theory. New York; John Wiley & Sons.

• Wilson, R. (1985). Introduction to Graph Theory. Harlow (U.K.): Longman.

Information on proof by mathematical induction is also helpful for this project. Check out our page on mathematical induction.

Subsets in Sequence Project Description |
Prerequisites | Warm Up Problems | Hints |
Resources | Teaching Notes | Extensions |
Results Making Mathematics Home |
Mathematics Projects | Students | Teachers |
Mentors | Parents | Hard Math Café |