031.js

// 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:

//    1x£1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p

// How many different ways can £2 be made using any number of coins?

var COINS = [1, 2, 5, 10, 20, 50, 100, 200];

function ways(sum) {
    var memo = [];
    for (var i = 0; i <= sum; i++) {
        memo[i] = 0;
    }
    memo[0] = 1;
    for (i = 0; i < COINS.length; i++) {
        for (var j = COINS[i]; j <= sum; j++) {
            memo[j] += memo[j - COINS[i]];
        }
    }
    return memo[sum];
}

console.log( ways(200) );