Question 51
For positive integers $n$, let $S_{n}$ be the set of integers $x$ such that $n$ distinct lines, no three concurrent, can divide a plane into $x$ regions (for example, $S_{2} = \{3, 4\}$, because the plane is divided into 3 regions if the two lines are parallel, and 4 regions otherwise). What is the minimum $i$ such that $S_{i}$ contains at least 4 elements?