MathDB

Let

n

be an integer greater than 1. The set

S

of all diagonals of a

\left( 4n-1\right)

-gon is partitioned into

k

sets,

S_{1},S_{2},\ldots ,S_{k},

so that, for every pair of distinct indices

i

and

j,

some diagonal in

S_{i}

crosses some diagonal in

S_{j};

that is, the two diagonals share an interior point. Determine the largest possible value of

k

in terms of

n.

Problem Statement