Difference between revisions of "1962 IMO Problems/Problem 1"
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=> <math>n = 15384</math>. | => <math>n = 15384</math>. | ||
− | => The original number = <math> | + | => The original number = <math>\boxed{153\,846}</math>. |
==See Also== | ==See Also== | ||
{{IMO box|year=1962|before=First Question|num-a=2}} | {{IMO box|year=1962|before=First Question|num-a=2}} |
Revision as of 00:51, 19 February 2022
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 |