## 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?

7652413

## Code: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;	}	}