**Problem:**

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 [→] 363601 [→] 1454 [→] 169

871 [→] 45361 [→] 871

872 [→] 45362 [→] 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 [→] 363600 [→] 1454 [→] 169 [→] 363601 ([→] 1454)

78 [→] 45360 [→] 871 [→] 45361 ([→] 871)

540 [→] 145 ([→] 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 [→] 363601 [→] 1454 [→] 169

871 [→] 45361 [→] 871

872 [→] 45362 [→] 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 [→] 363600 [→] 1454 [→] 169 [→] 363601 ([→] 1454)

78 [→] 45360 [→] 871 [→] 45361 ([→] 871)

540 [→] 145 ([→] 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?

**Solution:**

2783915460

**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 24

* By Nayuki Minase

*

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

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

*/

public final class p024 implements EulerSolution {

public static void main(String[] args) {

System.out.println(new p024().run());

}

public String run() {

// Initialize

int[] array = new int[10];

for (int i = 0; i < array.length; i++)

array[i] = i;

// Permute

for (int i = 0; i < 999999; i++) {

if (!Library.nextPermutation(array))

throw new AssertionError();

}

// Format output

String ans = "";

for (int i = 0; i < array.length; i++)

ans += array[i];

return ans;

}

}

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