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id	title	challengeType	forumTopicId	dashedName
5900f38b1000cf542c50fe9e	Problem 31: Coin sums	5	301965	problem-31-coin-sums

--description--

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p

How many different ways can n pence be made using any number of coins?

--hints--

coinSums(50) should return a number.

assert(typeof coinSums(50) === 'number');

coinSums(50) should return 451.

assert(coinSums(50) == 451);

coinSums(100) should return 4563.

assert(coinSums(100) == 4563);

coinSums(150) should return 21873.

assert(coinSums(150) == 21873);

coinSums(200) should return 73682.

assert(coinSums(200) == 73682);

--seed--

--seed-contents--

function coinSums(n) {

  return n;
}

coinSums(200);

--solutions--

const coinSums = (n) => {
  const getWays = (n, m=8, c=[1, 2, 5, 10, 20, 50, 100, 200]) => {
    if (n === 0) return 1;
    if (m === 0 || n < 0) return 0;
    return getWays(n - c[m - 1], m, c) + getWays(n, m - 1, c);
  };
  return getWays(n);
};

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