Resources for the Trains Problem
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
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 email@example.com).
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
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)