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So I was wondering, in the UK we have 1p, 2p, 5p, 10p, 20p, 50p and £1 coins. I came up with an answer for how many ways we could use all these coins to make up £1, which was 4563. Then I started thinking say we had £1.04 instead. How many ways could we do that. Basically say we have any amount X, how many ways can we do it. I started looking at the general problem and it seemed very tedious and tricky but certainly can be done. Looked online and can’t find anything. On this, just was an interesting problem to me. Is there any easy way to do this? I imagine there must be some algebra out there that makes answering this relatively easy.

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