**Problem:**

The points P (x1, y1) and Q (x2, y2) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,

0 [≤] x1, y1, x2, y2 [≤] 2.

Given that 0 [≤] x1, y1, x2, y2 [≤] 50, how many right triangles can be formed?

There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,

0 [≤] x1, y1, x2, y2 [≤] 2.

Given that 0 [≤] x1, y1, x2, y2 [≤] 50, how many right triangles can be formed?

**Solution:**

7652413

**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 41

* By Nayuki Minase

*

* http://nayuki.eigenstate.org/page/project-euler-solutions

* https://github.com/nayuki/Project-Euler-solutions

*/

public final class p041 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p041().run());

}

public String run() {

for (int n = 9; n >= 1; n--) {

int[] digits = new int[n];

for (int i = 0; i < digits.length; i++)

digits[i] = i + 1;

int result = -1;

do {

if (Library.isPrime(toInteger(digits)))

result = toInteger(digits);

} while (Library.nextPermutation(digits));

if (result != -1)

return Integer.toString(result);

}

throw new RuntimeException("Not found");

}

private static int toInteger(int[] digits) {

int result = 0;

for (int x : digits)

result = result * 10 + x;

return result;

}

}

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