**Problem:**

Consider the isosceles triangle with base length, b = 16, and legs, L = 17.

By using the Pythagorean theorem it can be seen that the height of the triangle, h = [√](172 [−] 82) = 15, which is one less than the base length.

With b = 272 and L = 305, we get h = 273, which is one more than the base length, and this is the second smallest isosceles triangle with the property that h = b [±] 1.

Find [∑] L for the twelve smallest isosceles triangles for which h = b [±] 1 and b, L are positive integers.

By using the Pythagorean theorem it can be seen that the height of the triangle, h = [√](172 [−] 82) = 15, which is one less than the base length.

With b = 272 and L = 305, we get h = 273, which is one more than the base length, and this is the second smallest isosceles triangle with the property that h = b [±] 1.

Find [∑] L for the twelve smallest isosceles triangles for which h = b [±] 1 and b, L are positive integers.

**Solution:**

932718654

**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 38

* By Nayuki Minase

*

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

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

*/

import java.util.Arrays;

public final class p038 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p038().run());

}

public String run() {

int max = -1;

for (int n = 2; n <= 9; n++) {

for (int i = 1; i < Library.pow(10, 9 / n); i++) {

String concat = "";

for (int j = 1; j <= n; j++)

concat += i * j;

if (isPandigital(concat))

max = Math.max(Integer.parseInt(concat), max);

}

}

return Integer.toString(max);

}

private static boolean isPandigital(String s) {

if (s.length() != 9)

return false;

char[] temp = s.toCharArray();

Arrays.sort(temp);

return new String(temp).equals("123456789");

}

}

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