Project Euler > Problem 139 > Pythagorean tiles (Java Solution)

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?

Solution:

840

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

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1	public interface EulerSolution{

2

3	public String run();

4

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}

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01

/*

02	* Solution to Project Euler problem 39

03	* By Nayuki Minase

04

*

05	* http://nayuki.eigenstate.org/page/project-euler-solutions

06	* https://github.com/nayuki/Project-Euler-solutions

07

*/

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09

10	public final class p039 implements EulerSolution {

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12	public static void main(String[] args) {

13	System.out.println(new p039().run());

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}

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17	public String run() {

18	int maxPerimeter = 0;

19	int maxTriangles = 0;

20	for (int p = 1; p <= 1000; p++) {

21	int triangles = countSolutions(p);

22	if (triangles > maxTriangles) {

23	maxTriangles = triangles;

24	maxPerimeter = p;

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}

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}

27	return Integer.toString(maxPerimeter);

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}

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30

31	private static int countSolutions(int p) {

32	int count = 0;

33	for (int a = 1; a <= p; a++) {

34	for (int b = a; b <= p; b++) {

35	int c = p - a - b;

36	if (b <= c && a * a + b * b == c * c)

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count++;

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}

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}

40	return count;

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}

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}