1962 IMO Problems/Problem 1
Find the smallest natural number 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 .
https://youtu.be/9y5UUNIhUfU?si=PzXbNokxOXCRxYBh [Video Solution by little-fermat]
As the new number starts with a and the old number is of the new number, the old number must start with a .
As the new number now starts with , the old number must start with .
We continue in this way until the process terminates with the new number and the old number .
Let the original number = , where is a 5 digit number.
Then we have .
=> The original number = .
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