In my last blog post I posed a question about finding the coeff of x^100 in a particular Taylor Series. The question and answer are given here:
The key to the problem was to recognize that it was asking how many ways you can make change of a dollar using pennies, nickels, dimes, and quarters. This can be done by hand (its 242).
1) Someone who I gave the problem to solved it by available software, but when he saw the answer was 242 he realized how to do it via making change.
2) How hard would this problem be to do completely by hand- say as a Putnam Problem? Its hard for me to say since I started with the trick and then found the problem.
3) Is this a well known trick?