8.9 (1) Two people, A and B, are playing a game: A writes two rows, each containing 10 numbers, such that they satisfy the following rule: if $b$ is below $a$, and $d$ is below $c$, then $a+d=b+c$. Knowing this rule, B wants to determine all the numbers written. B can ask A questions like, "What is the number in the third position of the first row?" or "What is the number in the ninth position of the second row?" and so on. How many such questions does B need to ask at least to know all the numbers?
(2) In an $m \times n$ grid filled with numbers, it is given that for any two rows and any two columns forming a rectangle, the sum of the numbers at the two opposite corners equals the sum of the numbers at the other two corners. Suppose that after erasing some of the numbers, the erased numbers can be restored based on the remaining numbers. Prove that the number of remaining numbers is at least $m+n-1$.
[Solution] It is easy to see that, knowing all 10 numbers in one row and one number in another row, it is possible to reconstruct all other numbers. If only 10 numbers are known, then either each column contains exactly one known number, or there is a column where both numbers are unknown. In the former case, any number $x$ can be taken as the difference between the two numbers in each column, and the other number in each column can be calculated based on the known number; in the latter case, adding any $x$ to both unknown numbers in the column still satisfies the requirement. Therefore, asking only 10 questions is not enough, and at least 11 questions are needed.

Below, we use mathematical induction to prove (2). Without loss of generality, assume $n \geqslant m$, and perform induction on $m+n$. If in any column no number is known, then the reconstruction of the numbers is clearly not unique. Below, assume that each column contains at least one known number. Since $m+n-2 \leqslant 2 n-2$, there must be a column with only one known number. Removing this column and applying the induction hypothesis shows that the reconstruction is not unique. This proves that $m+n-2$ known numbers are not enough.