**Problem:**

Some positive integers n have the property that the sum [ n + reverse(n) ] consists entirely of odd (decimal) digits. For instance, 36 + 63 = 99 and 409 + 904 = 1313. We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either n or reverse(n).

There are 120 reversible numbers below one-thousand.

How many reversible numbers are there below one-billion (109)?

There are 120 reversible numbers below one-thousand.

How many reversible numbers are there below one-billion (109)?

**Solution:**

1533776805

**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 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++;

}

}

}

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