olymmath

MEMO 2018 I2

    The two figures depicted below consisting of 66 and 1010 unit squares, respectively, are called staircases. Consider a 2018×20182018\times 2018 board consisting of 201822018^2 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).

    Attachments:

    sqing 2018.jpg

    Dataset text AI-MO AoPS. Quoted with source.

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