A finite set $\mathcal{L}$ of coplanar lines, no three of which are concurrent, is called odd if, for every line $\ell$ in $\mathcal{L}$ the total number of lines in $\mathcal{L}$ crossed by $\ell$ is odd. Prove that every finite set of coplanar lines, no three of which are concurrent, extends to an odd set of coplanar lines. Given a positive integer $n$ determine the smallest nonnegative integer $k$ satisfying the following condition: Every set of $n$ coplanar lines, no three of which are concurrent, extends to an odd set of $n+k$ coplanar lines.