Question 4
Consider the sequence of strings $0;\ 01;\ 0110;\ 01101001;\ 0110100110010110;\ldots$. Each new string is formed by appending the complement of the previous string, obtained by swapping $0$ and $1$. For example, the complement of $0110$ is $1001$, giving the next string $01101001$. The twelfth string has $2048$ digits. What is its $2016$th digit, counted from the left?
