Difference between revisions of "1990 AIME Problems/Problem 13"
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Revision as of 18:19, 4 July 2013
Problem
Let 
. Given that 
has 3817 digits and that its first (leftmost) digit is 9, how many elements of 
have 9 as their leftmost digit?
Solution
Whenever you multiply a number by 
, the number will have an additional digit over the previous digit, with the exception when the new number starts with a , when the number of digits remain the same. Since 
has 3816 digits more than 
, exactly 
numbers have 9 as their leftmost digits.
See also
| 1990 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
