9. (12 points) As shown in the figure, a $6 \times 6$ grid is divided into 9 blocks by thick lines. If a block contains exactly $N$ cells, then the numbers filled in that block are exactly $1 \sim N$; and any two adjacent cells (two small squares that share a common point are called adjacent cells) must have different numbers. What is the four-digit number $\overline{\mathrm{ABCD}}$?
4252
【Solution】According to the analysis, first, we can determine that the position $H$ with only one cell can only be filled with 1; the block where $B$ is located has only 2 cells, which can only be filled with 1 and 2, and since $B$ is adjacent to 1, it can only be filled with 2; $A$ can only be filled with 3 or 4, and the three cells below $B$ can only be filled with 1, 2, 3, so $A$ can only be filled with 4, because the cell at $E$ can only be filled with 1, and the cell at $I$ can only be filled with 3, then $C$ is filled with 5, and $D$ is filled with 2. The filling method is shown in the figure below:
In summary, $A: 4, B: 2, C: 5, D: 2$.
Therefore, the answer is: 4252.