##
**Problem:**

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p [≤] 1000, is the number of solutions maximised?

##
**Solution:**

840

##
**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 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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