1990 AIME Problems/Problem 13
From AoPSWiki
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 • Resources) | ||
| Preceded by Problem 12 | Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
