## 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?

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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