You can use rods of integer sizes to build "trains" that all share a common length. A "train of length 5" is a row of rods whose combined length is 5. Here are some examples: Notice that the 1-2-2 train and the 2-1-2 train contain the same rods but are listed separately. If you use identical rods in a different order, this is a separate train. How many trains of length 5 are there? Come up with a formula for the number of trains of length n. (Assume you have rods of every possible integer length available.) Prove that your formula is correct. Come up with an algorithm that will generate all the trains of length n. You can use Trains as a warm up for The Simplex Lock. Making Mathematics Home | Mathematics Projects | Students | Teachers | Mentors | Parents | Hard Math Café | Trains Project Description | Prerequisites | Warm Up Problems | Hints | Resources | Teaching Notes | Extensions | Results |
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