MathDB
1x2 in 2011x2011

Source: 2011 Cuba MO 1.3

September 18, 2024
combinatoricscombinatorial geometrytiles

Problem Statement

We have a board of 2011×2011 2011 \times 2011, divided by lines parallel to the edges into 1×11 \times 1 squares. Manuel, Reinaldo and Jorge (at that time order) play to form squares with vertices at the vertices of the grid. The one who forms the last possible square wins, so that its sides do not cut the sides of any unit square. Who can be sure that he will win?