IMO Shortlist 2012 problem C3
Dodao/la:
arhiva3. studenoga 2013. In a
![999 \times 999](/media/m/e/a/e/eaeb01b68a6b8561d2528310e2593c70.png)
square table some cells are white and the remaining ones are red. Let
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
be the number of triples
![(C_1,C_2,C_3)](/media/m/e/0/5/e0501c1fbd2b613e763a659ed19d2d58.png)
of cells, the first two in the same row and the last two in the same column, with
![C_1,C_3](/media/m/1/4/2/1421acc9c80d346ae8efc1c55bcfe4c5.png)
white and
![C_2](/media/m/a/b/8/ab898e857261e1c35339f3f3d8362ba0.png)
red. Find the maximum value
![T](/media/m/0/1/6/016d42c58f7f5f06bdf8af6b85141914.png)
can attain.
%V0
In a $999 \times 999$ square table some cells are white and the remaining ones are red. Let $T$ be the number of triples $(C_1,C_2,C_3)$ of cells, the first two in the same row and the last two in the same column, with $C_1,C_3$ white and $C_2$ red. Find the maximum value $T$ can attain.
Izvor: Međunarodna matematička olimpijada, shortlist 2012