**Question: **Find the smallest number N which has the following properties:

1. its decimal representation has 6 as the last digit.

2. If the last digit 6 is erased and placed in front of the remaining digits, the resulting number is four times as great as the original number N.

**Answer:**

The smallest such number is 153846.

Assume that the number N is

N = BnBn-1Bn-2 ... B3B26

as its given that 6 is the last digit.

Now after erasing 6 and putting it in front of the remaining digits, we get

Nnew = 6BnBn-1Bn-2 ... B3B2

Also given that Nnew is 4 times the N. Also note that the last digit Nnew is second last digit of N and so on. The required result is

BnBn-1Bn-2 ... B3B26

X 4

--------------------

6BnBn-1Bn-2 ... B3B2

So start multiplying and put nth digit of Nnew to (n + 1)th digit of N and you will get result as

1 5 3 8 4 6

X 4

---------------

6 1 5 3 8 4

Hence, the number is 153846