7. In archery, the score for each shot is either "0" (miss) or a natural number not exceeding 10. Athletes A and B each shot 5 arrows, and the product of the scores for each of their 5 arrows is 1764. However, Athlete A's total score is 4 points less than Athlete B's. Find the total scores of Athlete A and B.
7.【Solution】 $\because$ The product of each person's scores $=1764 \neq 0$,
$\therefore$ Neither of the two people hit a score of “0” or “10” with any arrow.
$\because$ Each score hit by an arrow is a factor of 1764, and: $1764=1 \times 2 \times 2 \times 3 \times 3 \times 7 \times 7$, and the scores are natural numbers not exceeding 10, $\therefore$ there must be two arrows that hit 7 points, and the scores of the other 3 arrows are factors of $1 \cdot 2 \cdot 2 \cdot 3 \cdot 3$.
If the smallest factor is 1, then the other two factors are 4 and 9, or 6 and 6; if the smallest factor is 2, then the other two factors are 2 and 9, or 3 and 6; if the smallest factor is 3, then the other two factors are 3 and 4.
Therefore, the scores of the two people's 5 arrows have 5 possible combinations:
$7,7,1,4,9$, sum $=28$;
$7,7,1,6,6$, sum $=27$;
$7,7,2,2,9$, sum $=27$;
$7,7,2,3,6$, sum $=25$;
$7,7,3,3,4$, sum $=24$;
$\because$ The total scores of A and B differ by 4, and A's total score is lower,
$\therefore$ A's total score is 24, and B's total score is 28.

Answer: The total scores of A and B are $24$ and $28$, respectively.