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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1997 AMC 12/AHSME
29
29
Part of
1997 AMC 12/AHSME
Problems
(1)
Special Numbers
Source:
1/18/2009
Call a positive real number special if it has a decimal representation that consists entirely of digits
0
0
0
and
7
7
7
. For example, \frac{700}{99} \equal{} 7.\overline{07} \equal{} 7.070707\cdots and
77.007
77.007
77.007
are special numbers. What is the smallest
n
n
n
such that
1
1
1
can be written as a sum of
n
n
n
special numbers?
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7
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8
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9
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D
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10
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The number 1 cannot be represented as a sum of finitely many special numbers.
<span class='latex-bold'>(A)</span>\ 7\qquad <span class='latex-bold'>(B)</span>\ 8\qquad <span class='latex-bold'>(C)</span>\ 9\qquad <span class='latex-bold'>(D)</span>\ 10\qquad\\ <span class='latex-bold'>(E)</span>\ \text{The number 1 cannot be represented as a sum of finitely many special numbers.}
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8
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9
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10
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The number 1 cannot be represented as a sum of finitely many special numbers.