## Problem:

Let (a, b, c) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length c.

For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.

However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square.

Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?

840

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

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 39 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p039 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p039().run());	}			public String run() {		int maxPerimeter = 0;		int maxTriangles = 0;		for (int p = 1; p <= 1000; p++) {			int triangles = countSolutions(p);			if (triangles > maxTriangles) {				maxTriangles = triangles;				maxPerimeter = p;			}		}		return Integer.toString(maxPerimeter);	}			private static int countSolutions(int p) {		int count = 0;		for (int a = 1; a <= p; a++) {			for (int b = a; b <= p; b++) {				int c = p - a - b;				if (b <= c && a * a + b * b == c * c)					count++;			}		}		return count;	}	}

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