II. (50 points) On an infinite grid paper, some cells are colored red, and the rest are colored blue. In every $2 \times$ 3 rectangle of six cells, there are exactly two red cells. How many red cells are there in a $9 \times 11$ rectangle of 99 cells?
II. Solution: 33 red squares. As shown in the figure, take any red square $K_{0}$ as the center of a $3 \times 3$ square; it is not possible to color $K$ red. If $K$ is colored red, then in the $2 \times 3$ rectangles $A F H D$, $A B S T$, and $M N C D$, there will be two red squares each. To ensure that the rectangle $B C G E$ contains two red squares, placing a red square anywhere will result in one of the aforementioned three rectangles having three red squares. This means that the red square cannot share a side with $K_{0}$, but must be on its diagonal, which is feasible overall. Therefore, each $3 \times 3$ square contains exactly 3 red squares. In the $9 \times 11$ rectangle, it can be divided into nine $3 \times 3$ squares and three $2 \times 3$ rectangles, so there are a total of 33 red squares.