Difference between revisions of "1997 AHSME Problems/Problem 29"

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==Problem==
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Call a positive real number special if it has a decimal representation that consists entirely of digits <math>0</math> and <math>7</math>. For example, <math> \frac{700}{99}= 7.\overline{07}= 7.070707\cdots </math> and <math> 77.007 </math> are special numbers. What is the smallest <math>n</math> such that <math>1</math> can be written as a sum of <math>n</math> special numbers?
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<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\\ \textbf{(E)}\ \text{The number 1 cannot be represented as a sum of finitely many special numbers.} </math>
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==Solution==
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== See also ==
 
== See also ==
 
{{AHSME box|year=1997|num-b=28|num-a=30}}
 
{{AHSME box|year=1997|num-b=28|num-a=30}}

Revision as of 18:12, 23 August 2011

Problem

Call a positive real number special if it has a decimal representation that consists entirely of digits $0$ and $7$. For example, $\frac{700}{99}= 7.\overline{07}= 7.070707\cdots$ and $77.007$ are special numbers. What is the smallest $n$ such that $1$ can be written as a sum of $n$ special numbers?

$\textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\\ \textbf{(E)}\ \text{The number 1 cannot be represented as a sum of finitely many special numbers.}$

Solution

See also

1997 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 28
Followed by
Problem 30
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