Difference between revisions of "1992 AIME Problems/Problem 5"
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== Problem == | == Problem == | ||
| + | Let <math>S^{}_{}</math> be the set of all rational numbers <math>r^{}_{}</math>, <math>0^{}_{}<r<1</math>, that have a repeating decimal expansion in the form <math>0.abcabcabc\ldots=0.\overline{abc}</math>, where the digits <math>a^{}_{}</math>, <math>b^{}_{}</math>, and <math>c^{}_{}</math> are not necessarily distinct. To write the elements of <math>S^{}_{}</math> as fractions in lowest terms, how many different numerators are required? | ||
== Solution == | == Solution == | ||
Revision as of 22:29, 10 March 2007
Problem
Let 
be the set of all rational numbers 
, 
, that have a repeating decimal expansion in the form 
, where the digits 
, 
, and 
are not necessarily distinct. To write the elements of as fractions in lowest terms, how many different numerators are required?
Solution
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