【Question 7】
In a certain mathematics competition, there are a total of 6 questions, each worth 7 points (the final score for each question is an integer, with a minimum of 0 points and a maximum of 7 points). Each contestant's total score is the product of the scores of the 6 questions. If two contestants have the same score, the sum of the scores of the 6 questions is used to determine the ranking. If they are still the same, the two contestants are ranked as tied. In this competition, there are a total of $8^{6}=262144$ contestants, and there are no ties among these contestants. The score of the contestant ranked $7^{6}=117649$ is $\qquad$ points.
【Explanation】
(1) This is a wrong question.

If two people have exactly the same scores for all 6 questions,
then the product of the scores for the 6 questions is the same, and the sum of the scores for the 6 questions is also the same;
thus, these two people have the same ranking, i.e., these two people are tied.
According to the problem, there are no ties among the $8^{6}=262144$ participants;
thus, the scores of the $8^{6}=262144$ participants for each question are not exactly the same.
The score for each question is an integer from $0 \sim 7$, and by the multiplication principle, there are $8^{6}$ possible score combinations;
if participant A's scores for questions $1 \sim 6$ are $0, 0, 0, 0, 0, 0, 1$, and participant B's scores for questions $1 \sim 6$ are $0, 0, 0, 0, 0, 1, 0$,
the product of the scores for the 6 questions for both A and B is 0, and the sum of the scores for the 6 questions is 1;
thus, A and B have the same ranking, i.e., these two people are tied;
this contradicts the statement that "there are no ties among these participants."
Therefore, this is a wrong question.
(2) If the original problem statement "there are no ties among these participants" is changed to "among these participants, the scores for each of the 6 questions for any two participants are not exactly the same," then the score of the participant ranked $7^{6}=117649$ is 1 point.
The reason is as follows:
If at least one of the 6 questions has a score of 0, then the product of the scores for the 6 questions is 0;
If none of the 6 questions has a score of 0, then the product of the scores for the 6 questions is not 0,
in this case, the score for each question is an integer from $1 \sim 7$, and by the multiplication principle, there are $7^{6}$ possible score combinations;
thus, the score of the participant ranked $7^{6}=117649$ is the smallest positive integer product;
and the participant whose scores for questions $1 \sim 6$ are $1, 1, 1, 1, 1, 1$ has a score of 1;
thus, the score of the participant ranked $7^{6}=117649$ is 1 point.