MathDB

Given an integer

n \geq 1

, Jo-Ané alternately writes crosses (

\mathcal{X}

) and circles (

\mathcal{O}

) in the cells of a square grid with

2n + 1

rows and

2n + 1

columns: she first writes a cross in a cell, then a circle in a second cell, then a cross in a third cell, and so on. When the table is completely filled, her score is calculated as the sum

\mathcal{X}+ \mathcal{O}

, where

\mathcal{X}

is the number of rows containing more crosses than circles and

\mathcal{O}

is the number of columns containing more circles than crosses.
Determine, in terms of

n

, the highest possible score that Jo-Ané can obtain..

Problem Statement