Difference between revisions of "2012 AMC 12A Problems/Problem 24"
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Revision as of 16:16, 19 February 2012
Problem
Let 
be the sequence of real numbers defined by 
, and in general,
![\[a_k=\begin{cases}(0.\underbrace{20101\cdots 0101}_{k+2\text{ digits}})^{a_{k-1}}\qquad\text{if }k\text{ is odd,}\\(0.\underbrace{20101\cdots 01011}_{k+2\text{ digits}})^{a_{k-1}}\qquad\text{if }k\text{ is even.}\end{cases}\]](http://latex.artofproblemsolving.com/0/0/6/006ecf77f807aa89b66a8e2e9f281e579e7cd062.png)
Rearranging the numbers in the sequence in decreasing order produces a new sequence 
. What is the sum of all integers 
, 
, such that 
$\textbf{(A)}\ 671\qquad\textbf{(B)}\ 1006\qquad\textbf{(C)}\ 1341\qquad\textbf{(D)}\ 2011\qquad\textbf{(E)}\2012$ (Error compiling LaTeX. Unknown error_msg)
Solution
| 2012 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 23 |
Followed by Problem 25 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
