## Counting Pennies, Generating Functions and STEP

STEP I 1997, Question 1 Show that you can make up 10 pence in eleven ways using 10p, 5p, 2p and 1p coins. In how many ways can you make up 20 pence using 20p,10p 5p, 2p and 1p coins? There is an interesting way of approaching this question using generating functions. A generating function …