Main.java

/*
@author: mc-es

Problem 39
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?

Answer: 840
*/

public class Main {
 public static void main(String[] args) {
 int maxSolutions = 0;
 int maxP = 0;

 for (int p = 1; p <= 1000; p++) {
 int solutions = countRightAngleTriangles(p);
 if (solutions > maxSolutions) {
 maxSolutions = solutions;
 maxP = p;
 }
 }

 System.out.println("p value with the most solutions: " + maxP);
 System.out.println("Number of solutions: " + maxSolutions);
 }

 public static int countRightAngleTriangles(int p) {
 int count = 0;
 for (int a = 1; a <= p / 3; a++) {
 for (int b = a; b <= (p - a) / 2; b++) {
 int c = p - a - b;
 if (a * a + b * b == c * c) {
 count++;
 }
 }
 }
 return count;
 }
}