Question 34
There are $2012$ students standing in a circle, numbered $1,2,\ldots,2012$ clockwise. Counting starts at student $1$ and goes clockwise. Alternate students are eliminated: student $1$ stays, student $2$ leaves, student $3$ stays, student $4$ leaves, and so on. After reaching $2012$, counting returns to $1$ and elimination continues until one student remains. What is that student's number?