**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?

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

**Solution:**

1074

**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 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}

};

}

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