1962 IMO Problems/Problem 1

Problem

Find the smallest natural number $n$ which has the following properties:

(a) Its decimal representation has 6 as the last digit.

(b) If the last digit 6 is erased and placed in front of the remaining digits, the resulting number is four times as large as the original number $n$.

Solution

As the new number starts with a $6$ and the old number is $1/4$ of the new number, the old number must start with a $1$.

As the new number now starts with $61$, the old number must start with $\lfloor 61/4\rfloor = 15$.

We continue in this way until the process terminates with the new number $615\,384$ and the old number $n=\boxed{153\,846}$.

See Also

1962 IMO (Problems) • Resources)
Preceded by
First Question
1 2 3 4 5 6 Followed by
Problem 2
All IMO Problems and Solutions
Invalid username
Login to AoPS