## Problem:

Using all of the digits 1 through 9 and concatenating them freely to form decimal integers, different sets can be formed. Interestingly with the set {2,5,47,89,631}, all of the elements belonging to it are prime.

How many distinct sets containing each of the digits one through nine exactly once contain only prime elements?

1074

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

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 18 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p018 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p018().run());	}			public String run() {		for (int i = triangle.length - 2; i >= 0; i--) {			for (int j = 0; j < triangle[i].length; j++)				triangle[i][j] += Math.max(triangle[i + 1][j], triangle[i + 1][j + 1]);  // Dynamic programming		}		return Integer.toString(triangle[0][0]);	}			private int[][] triangle = {		{75},		{95,64},		{17,47,82},		{18,35,87,10},		{20,04,82,47,65},		{19,01,23,75,03,34},		{88,02,77,73,07,63,67},		{99,65,04,28,06,16,70,92},		{41,41,26,56,83,40,80,70,33},		{41,48,72,33,47,32,37,16,94,29},		{53,71,44,65,25,43,91,52,97,51,14},		{70,11,33,28,77,73,17,78,39,68,17,57},		{91,71,52,38,17,14,91,43,58,50,27,29,48},		{63,66,04,68,89,53,67,30,73,16,69,87,40,31},		{04,62,98,27,23, 9,70,98,73,93,38,53,60,04,23}	};	}