3. (10 points) Four pieces of paper with 4 squares each, as shown in Figure 1, are used to form the shape shown in Figure 2. If the numbers $1, 3, 5, 7$ (one number per square) are filled into the 16 squares in Figure 2, such that no number is repeated in any row, column, or within any of the four pieces of paper, then the average of the numbers in the squares $A, B, C, D$ is ( )
A. 4
B. 5
C. 6
D. 7
【Analysis】As shown in Figure 2,
According to the rule that the four numbers in each cardboard do not repeat, we can get: $A$ $\neq E, A \neq F, B \neq E, B \neq F$, so $A=G, B=H$ or $A=H, B=G$, so $G+H=A+B$, based on this, we need to find the average of the numbers in the four squares $A, B, C, D$.

【Solution】As shown in Figure 2,
Because the four numbers in each cardboard do not repeat,
So $A \neq E, A \neq F, B \neq E, B \neq F$,
So $A=G, B=H$ or $A=H, B=G$,
So $G+H=A+B$,
So the numbers in the four squares $A, B, C, D$ are $1,3,5,7$ (each square is filled with one number),
So the average of the numbers in the four squares $A, B, C, D$ is:
$$
(1+3+5+7) \div 4=4 \text {. }
$$

Answer: The average of the numbers in the four squares $A, B, C, D$ is 4.
Therefore, the correct answer is: A.