# Colorful Numbers

Objective: Given a number, find out whether its colorful or not.

Colorful Number: When in a given number, product of every digit of a sub-sequence are different. That number is called Colorful Number. See Example

Example:

```Given Number : 3245
Output : Colorful
Number 3245 can be broken into parts like 3 2 4 5 32 24 45 324 245.
this number is a colorful number, since product of every digit of a sub-sequence are different.
That is, 3 2 4 5 (3*2)=6 (2*4)=8 (4*5)=20, (3*2*4)= 24 (2*4*5)= 40

Given Number : 326
Output : Not Colorful.
326 is not a colorful number as it generates 3 2 6 (3*2)=6 (2*6)=12.
```

Reference : http://www.careercup.com/question?id=4863869499473920

Approach:

• Insert all the digits into hast table
• Create a powerset of digits except empty set (Power Set)
• Multiply all the digits in the individual powerset and insert into Hash Table.
• If any point, number already present in the Hash table, return false

Code:

Output:

```326 Colorful?? false
3245 Colorful?? true
```

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.
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