# 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 : 3245Output : ColorfulNumber 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 : 326Output : 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