MathDB

Given

2009 \times 4018

rectangular board. Frame is a rectangle

n \times n

n \times(n + 2)

for

( n \geq 3 )

without all cells which don’t have any common points with boundary of rectangle. Rectangles

1\times1,1\times 2,1\times 3

and

2\times 4

are also frames. Two players by turn paint all cells of some frame that has no painted cells yet. Player that can't make such move loses. Who has a winning strategy?

Problem Statement