Difference between revisions of "Mock AIME 2 Pre 2005 Problems/Problem 4"
(Created page with "== Problem == Let <math>S = \{5^k | k \in \mathbb{Z}, 0 \le k \le 2004 \}</math>. Given that <math>5^{2004} = 5443 \cdots 0625</math> has <math>1401</math> digits, how many e...") |
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Revision as of 17:15, 4 August 2019
Problem
Let . Given that has digits, how many elements of begin with the digit ?
Solution
Note that has the same number of digits as if and only if has a leading digit . Therefore, there are numbers with leading digit among the set However, also starts with , so the answer is .
See also
Mock AIME 2 Pre 2005 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |