MEMO 2017 ekipno problem 3

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Dodao/la: arhiva
12. rujna 2018.

There is a lamp on each cell of a 2017 \times 2017 board. Each lamp is either on or off. A lamp is called bad if it has an even number of neighbours that are on. What is the smallest possible number of bad lamps on such a board?
(Two lamps are neighbours if their respective cells share a side.)

Izvor: Srednjoeuropska matematička olimpijada 2017, ekipno natjecanje, problem 3