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