Resources for the Trains Problem

Manipulatives

If you want to work with actual rods, Cuisenaire rods are a nice choice. The 1-rod is a cube, and the other rods (lengths 2-10) have the same width and height, and integer lengths. You can order them from Cuisenaire/ETA. Their web site is http://www.cuisenaire.com/.

Combinations and Permutations

Education Development Center, Inc., Mathematical Methods in High School, (in preparation http://www.edc.org/LTT/M2HS/, for more information contact Helen Lebowitz at hlebowitz@edc.org).

Rosen, Kenneth L., Discrete Mathematics and Its Applications, WCB McGraw-Hill, 1999. pp 250-260

Graham, R.L., D.E. Knuth, O. Patasknik, Concrete Mathematics, Addison-Wesley Publishing Company, 1992. pp153-163

Partitions

Andrews, G.E., Number Theory, Dover Publishing, 1994. Chapters 12-14.

You can download a beautiful paper on partitions by Herbert Wilf as a PDF (Adobe Acrobat) file: http://www.math.upenn.edu/~wilf/PIMS/PIMSLectures.pdf.