MathDB

Let

n \geq 2

be a natural number. We consider a

(2n - 1) \times (2n - 1)

table.Ana and Bob play the following game: starting with Ana, the two of them alternately color the vertices of the unit squares, Ana with red and Bob with blue, in

2n^2

rounds. Then, starting with Ana, each one forms a vector with origin at a red point and ending at a blue point, resulting in

2n^2

vectors with distinct origins and endpoints. If the sum of these vectors is zero, Ana wins. Otherwise, Bob wins. Show that Bob has a winning strategy.

Problem Statement