Suppose, $N$ random digits have been generated. Let $X$ be the largest natural number with the following property :
There are natural numbers $i$ and $j$ with $i+X-1<j$ , such that the digits $i$ to $i+X-1$ are the same digits as the digits $j$ to $j+X-1$. So, the digits $i+m$ and $j+m$ are equal for $0\le m\le X-1$. In other words, a block of $X$ digits appears at least twice (and the identical blocks are seperated).
It is clear that $X\ge 1$ holds, if $N>10$.
- What is E(X) depending on N ?