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Problem 31

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Coin sums

In England the currency is made up of pound, $\it\unicode{xA3}$, and pence, $p$, and there are eight coins in general circulation:
$$1p, 2p, 5p, 10p, 20p, 50p, {\it\unicode{xA3}}1(100p), {\it\unicode{xA3}}2(200p)$$

It is possible to make ${\it\unicode{xA3}}2$ in the following way:
$$1\times {\it\unicode{xA3}}1+ 1\times 50p + 2 \times 20 p+1\times 5p+ 1\times 2p+3\times 1p$$

How many different ways can ${\it\unicode{xA3}}2$ be made using any number of coins?

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硬币求和

英国的货币单位分英镑$\it\unicode{xA3}$和便士$p$，目前流通的硬币一共有八种面值：
$$1p, 2p, 5p, 10p, 20p, 50p, {\it\unicode{xA3}}1(100p), {\it\unicode{xA3}}2(200p)$$

想要凑出${\it\unicode{xA3}}2$，其中一种做法是：
$$1\times {\it\unicode{xA3}}1+ 1\times 50p + 2 \times 20 p+1\times 5p+ 1\times 2p+3\times 1p$$

不限制硬币数量，凑出${\it\unicode{xA3}}2$有多少种不同的做法？

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