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 19:12, 23 August 2011
Problem
Call a positive real number special if it has a decimal representation that consists entirely of digits 
and 
. For example, 
and 
are special numbers. What is the smallest 
such that 
can be written as a sum of special numbers?
Solution
See also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
