Permutiple | Topcoder Archive

Problem Statement

You are given a positive integer x. Please check whether we can rearrange the digits of x (in base 10, without leading zeros) to produce a different number that is a multiple of x.

Return "Possible" if this can be done and "Impossible" otherwise. Note that the return value is case-sensitive.

Definition

Class:: Permutiple
Method:: isPossible
Parameters:: int
Returns:: String
Method signature:: String isPossible(int x)
(be sure your method is public)

Constraints

x will be between 1 and 1,000,000, inclusive.

Examples

```
142857
```
```
Returns: "Possible"
```
One valid way of rearranging the digits of 142857 is to form the number 285714. This new number is a multiple of x: we have 285714 = 2 * 142857. Another valid way is to form the number 857142 (which is equal to 6 * 142857).
```
14
```
```
Returns: "Impossible"
```
The only other number we can get by rearranging the digits of the number 14 is the number 41. As 41 is not a multiple of 14, there is no solution.
```
1035
```
```
Returns: "Possible"
```
We can get 3105 = 3 * 1035.
```
1000000
```
```
Returns: "Impossible"
```
```
100035
```
```
Returns: "Possible"
```
```
4
```
```
Returns: "Impossible"
```

This problem statement is the exclusive and proprietary property of Topcoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of Topcoder, Inc. is strictly prohibited. (c)2024, Topcoder, Inc. All rights reserved.