Homework for Math 497
due Wed 10/29
Part 1: Consolidation
You have done some of this already. To the extent that you have, you can just use what you have done.
Look at the counting problems for trains in earlier sessions and come up with a little list of kinds of train problems (for example (1) total number of trains of length n (2) total number of trains of length n made of cars of length 1 or 2, …
Then tell for each kind
What is the answer to the counting problem? Answer in general if you can.
What problem numbers are train-counting problems of this type?
Given some examples of other problems (ice cream, committees, trips, polynomials) that are really the same problem in another guise.
Please make this something like a readable little essay.
Part 2: Some problems
2A: I wrote on the board last time a set of sums obtained by adding numbers on a diagonal in the Pascal triangle. So I was adding by starting at row n and column 0, then moving up one and one to the right (i.e, decrease the row number by one and add one to the column number). This turned out to be a familiar sequence of numbers. Give an explanation why this works.
2B: Do Problem 97, including the epiphany bit if you have one.
2C: Write up problems 68 and 69