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I remember reading SICP. It's a lot of fun. The recursive algorithm reminds me of something I was just looking at the other day, the Chu-Vandermonde identity. One obvious way to speed it up is memoization. But I wonder if that would be as effective in this case as for Fibonacci. Another way would be to just handle the penny case by just outputting 1 straight away if amount >= 0, and handle the penny-and-nickel case by outputting 1+floor(amount/5). I'd imagine that just doing this would speed up the program quite a bit. But a straight-up, non-recursive calculation in one fell swoop? I'm not sure how to do that.