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**Problem:**

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 £2 be made using any number of coins?

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**Solution:**

73682

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**Code:**

The solution may include methods that will be found here: Library.java .

The solution may include methods that will be found here: Library.java .

public interface EulerSolution{ public String run(); }

/* * Solution to Project Euler problem 31 * By Nayuki Minase * * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */ public final class p031 implements EulerSolution { public static void main(String[] args) { System.out.println(new p031().run()); } private static final int TOTAL = 200; private static int[] COINS = {1, 2, 5, 10, 20, 50, 100, 200}; public String run() { // Knapsack problem. ways[i][j] is the number of ways to use // any of the first i coin values to form an unordered sum of j. int[][] ways = new int[COINS.length + 1][TOTAL + 1]; ways[0][0] = 1; for (int i = 0; i < COINS.length; i++) { for (int j = 0; j <= TOTAL; j++) ways[i + 1][j] = ways[i][j] + (j >= COINS[i] ? ways[i + 1][j - COINS[i]] : 0); // Dynamic programming } return Integer.toString(ways[COINS.length][TOTAL]); } }

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