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Does there exists a real p such that f(n)/n ≥ p for all n?

Source: IMO LongList 1970 - P49

May 22, 2011
limitnumber theory proposednumber theory

Problem Statement

For n∈Nn \in \mathbb N, let f(n)f(n) be the number of positive integers k≤nk \leq n that do not contain the digit 99. Does there exist a positive real number pp such that f(n)n≥p\frac{f(n)}{n} \geq p for all positive integers nn?
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