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Trains Project Description Prerequisites Warm up Problems Hints Resources Teaching Notes Extension Problems Results

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.

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