MathDB

A finite set

\mathcal{L}

of coplanar lines, no three of which are concurrent, is called odd if, for every line

\ell

\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.

Problem Statement