MEMO 2018 pojedinačno problem 2


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8. rujna 2018.
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The two figures depicted below, consisting of 6 and 10 unit sqares respectively are called staircases.

Attachment #1

Consider a 2018 \times 2018 board consisting of 2018^2 cells, each being an 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).

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Screenshotfrom2018-09-0822-45-34.png 4,8 KB
Izvor: Srednjoeuropska matematička olimpijada 2016, pojedinačno natjecanje, problem 2