Marinada '26

[lang=hr] Svi kvadratići tablice $1000 \times 1000$ obojeni su crno ili bijelo, pri čemu postoji kvadrat $10 \times 10$ čiji su svi kvadratići crni, kao i kvadrat $10 \times 10$ čiji su svi kvadratići bijeli. Za svaki kvadrat $K$ dimenzija $10 \times 10$ definiramo $b(K)$ kao apsolutnu vrijednost razlike broja crnih i bijelih polja u kvadratu $K$. Neka je $T$ kvadrat $10 \times 10$ koji ima najmanju vrijednost $b(T)$. Odredite najveću moguću vrijednost $b(T)$. [/lang] [lang=en] All cells of a $1000 \times 1000$ board are coloured either black or white, such that there exists a $10 \times 10$ square whose cells are all black, as well as a $10 \times 10$ square whose cells are all white. For every $10 \times 10$ square $K$, we define $b(K)$ as the absolute value of the difference between the number of black and white cells in the square $K$. Let $T$ be a $10 \times 10$ square with the minimum value of $b(T)$. Determine the maximum possible value of $b(T)$. [/lang]