Overcounting

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Description

Overcounting is the process of counting more than what you need and then systematically subtracting the parts which do not belong.

Example

Let S be the set of all rational numbers ${r}$, $0 < r < 1$, that have a repeating decimal expansion in the form $0.abcabcabc\dots$, where the digits a, b, and c are not necessarily distinct. To write the elements of S as fractions in lowest terms, how many numerators are required?

(Solution Coming)

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