MathNet 2006 — Part 03 Question 124

Let $S$ be the set of all those $2007$-place decimal integers $\overline{2a_1a_2a_3\cdots a_{2006}}$ which contain odd number of digit '9' in each sequence $a_1, a_2, a_3, \cdots, a_{2006}$. The cardinal number of $S$ is