Solution
Ten Lines
Show the problem again
Ten lines are drawn in the plane so that no two are parallel and no three pass through a common point. Into how many regions do they divide the plane? Give an integer.
Worked solution
The answer is 56. When the $k$-th line is added, it crosses the previous $k - 1$ lines at $k - 1$ distinct points, which cut it into $k$ pieces. Each piece splits one existing region in two, so the $k$-th line adds $k$ regions. Starting from 1 region, ten lines give $1 + (1 + 2 + \dots + 10) = 1 + 55 = 56$. In general $n$ lines in general position give $1 + n + \binom{n}{2}$ regions.
Source: The "lazy caterer" sequence; classic exercise in wide circulation. Statement written for AxiomIQ.