How many different ways can you make change for $1, given quarters and dimes? What about the general case with some amount and a list of different types of coins? The key observation is that we can divide the solutions into two parts: those that requires the first coin and those that don't. From this observation a recursive function "count" can be devised, with count(money, coins.tail) + count(money-coins.head, coins), together with some common sense base cases, will show how many ways we can make change. (86 words)
