MathDB

The two figures depicted below consisting of

6

and

10

unit squares, respectively, are called staircases. Consider a

2018\times 2018

board consisting of

2018^2

cells, each being a unit square. Two arbitrary cells were removed from the same row of the board. Prove that the rest of the board cannot be cut (along the cell borders) into staircases (possibly rotated).

Problem Statement