Project Euler > Problem 45 > Triangular, pentagonal, and hexagonal (Java Solution)

Problem:

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle Tn=n(n+1)/2 1, 3, 6, 10, 15, ...
Pentagonal Pn=n(3n[−]1)/2 1, 5, 12, 22, 35, ...
Hexagonal Hn=n(2n[−]1) 1, 6, 15, 28, 45, ...

It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

Solution:

1533776805

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

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 45
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p045 implements EulerSolution {
 
 public static void main(String[] args) {
  System.out.println(new p045().run());
 }
 
 
 public String run() {
  int i = 286;
  int j = 166;
  int k = 144;
  while (true) {
   long triangle = (long)i * (i + 1) / 2;
   long pentagon = (long)j * (j * 3 - 1) / 2;
   long hexagon  = (long)k * (k * 2 - 1);
   long min = Math.min(Math.min(triangle, pentagon), hexagon);
   if (min == triangle && min == pentagon && min == hexagon)
    return Long.toString(min);
   if (min == triangle) i++;
   if (min == pentagon) j++;
   if (min == hexagon ) k++;
  }
 }
 
}