Difference between revisions of "1962 IMO Problems/Problem 1"
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(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 <math>n</math>. | (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 <math>n</math>. | ||
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+ | ==Video Solution== | ||
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+ | https://youtu.be/9y5UUNIhUfU?si=PzXbNokxOXCRxYBh | ||
+ | [Video Solution by little-fermat] | ||
==Solution 1== | ==Solution 1== |
Latest revision as of 23:36, 3 September 2023
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 .
Video Solution
https://youtu.be/9y5UUNIhUfU?si=PzXbNokxOXCRxYBh [Video Solution by little-fermat]
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 |