3.48 Let a $10 \times 10$ grid table $A$ contain an integer in each cell. Denote the sum of the numbers in the $i$-th row as $s_{i}$, and the sum of the numbers in the $j$-th column as $t_{j}, i, j=1,2, \cdots, 10$. Then fill a new $10 \times 10$ grid table $B$ in the following way: in the cell at the $i$-th row and $j$-th column, write the smaller of $s_{i}$ and $t_{j}$. It is known that the cells in table $B$ can be numbered from 1 to 100 such that the number in the $k$-th cell is no greater than $k$. Find the maximum possible sum of all the numbers in table $A$.
［Solution］Assume without loss of generality that $s_{1} \leqslant s_{2} \leqslant \cdots \leqslant s_{10}, t_{1} \leqslant t_{2} \leqslant \cdots \leqslant t_{10}, s_{10} \leqslant t_{10}$, and let the element in the $i$-th row and $j$-th column of table $B$ be denoted as $b_{i j}$. According to the given information, we have
$$
b_{i 10}=\min \left\{s_{i}, t_{10}\right\}=s_{i}, i=1,2, \cdots, 10 .
$$

Thus, the sum of all numbers in table $A$ is $s=\sum_{i=1}^{10} s_{i}=\sum_{i=1}^{10} b_{i 10}$. Since $b_{110}, b_{210}, \cdots, b_{1010}$ are 10 numbers in table $B$, their sum does not exceed the sum of the largest 10 numbers in $B$, hence $\sum_{i=1}^{10} b_{i 10} \leqslant 955$, which means the sum of all numbers in table $A$ does not exceed 955.

On the other hand, when table $A$ is as shown in the figure on the right, the sum of all its numbers is 955, and the derived table $B$ is identical to $A$, which of course meets the requirements of the problem.

In summary, the maximum value of the sum of all numbers in table $A$ is 955.