Vrijeme: 02:09

Optimizacija ploče | Board Optimization #1

Ploča 2021 \times 100 (2021 redaka i 100 stupaca) pobojena je šahovski. Figura zvana skakavac napada sva polja u istom retku koja su iste boje kao i polje skakavca, kao i sva polja u istom stupcu koja su suprotne boje od polja skakavca (skakavcu je dozvoljeno da preskače druge figure). Koji je najveći broj skakavaca koji je moguće postaviti na ploču tako da se međusobno ne napdaju?
A 2021 \times 100 board (2021 rows and 100 columns) is colored in the checkerboard pattern. A piece called a grasshopper attacks all squares in its row that are of the same color as the square it stands on, as well as all squares in its column of the opposite color (the grasshopper piece is allowed to jump over other pieces). What is the largest number of grasshoppers that can be placed on the board in such a way that none of them attack each other?