Difference between revisions of "1990 AIME Problems/Problem 13"

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== Problem ==
 
== Problem ==
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Let <math>T = \{9^k : k ~ \mbox{is an integer}, 0 \le k \le 4000\}</math>.  Given that <math>9^{4000}_{}</math> has 3817 digits and that its first (leftmost) digit is 9, how many elements of <math>T_{}^{}</math> have 9 as their leftmost digit?
  
 
== Solution ==
 
== Solution ==
 
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== See also ==
 
== See also ==
* [[1990 AIME Problems]]
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{{AIME box|year=1990|num-b=12|num-a=14}}

Revision as of 00:38, 2 March 2007

Problem

Let $T = \{9^k : k ~ \mbox{is an integer}, 0 \le k \le 4000\}$. Given that $9^{4000}_{}$ has 3817 digits and that its first (leftmost) digit is 9, how many elements of $T_{}^{}$ have 9 as their leftmost digit?

Solution

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See also

1990 AIME (ProblemsAnswer KeyResources)
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