Example 5 Lift Your Veil
A 101-digit natural number $A=\underbrace{88 \cdots 8}_{\text {S0 digits }} \square \underbrace{99 \cdots 9}_{\text {S0 digits }}$ is divisible by 7. What is the digit covered by $\square$?
Explanation: “ $\square$ ” is a veil, covering the number to be found. To lift the veil, whether approaching from the front or the back, there are 50 digits in between, which is too many. The key is to find a way to reduce the number of digits.

The difference between two multiples of 7 is still a multiple of 7.
We already know that $A$ is a multiple of 7.
Find another multiple of 7, $B$, such that all its digits are 1. Through trial division, we find
$$
B=111111=7 \times 15873 .
$$

From this, we see that $8 B=888888$ and $9 B=999999$ are also multiples of 7.

Removing 888888 from the front of the number $A$ is equivalent to subtracting $88888800 \cdots 0$ (95 zeros) from $A$. Therefore, the resulting number is still a multiple of 7.

Continuing this process, we can remove 6 eights from the front each time, until a total of 48 eights have been removed.

Similarly, we can remove 6 nines from the back of $A$ each time, until a total of 48 nines have been removed.
Finally, a 5-digit number 88 $\square$ 99 remains, which is a multiple of 7.

The problem is simplified to finding a 5-digit number $C$, which starts with 88 and ends with 99, and is a multiple of 7. The result is
$$
\begin{aligned}
C & =(49+350)+(84000+4200) \\
& =88599 .
\end{aligned}
$$

Therefore, the digit covered by $\square$ is 5.