1962 IMO Problems/Problem 1
Contents
Problem
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 .
Solution 1
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 .
Solution 2
Let the original number = , where is a 5 digit number.
Then we have .
=> .
=> .
=> .
=> The original number = .
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 |