6. Viewers rate a movie with an integer number of points from 0 to 10. At any given time, the movie's rating is calculated as the sum of all the given ratings divided by their number. At some point in time $T$, the rating was an integer, and then with each new voting viewer, it decreased by one. What is the maximum number of viewers who could have voted after moment $T$? (O. Dmitriev, R. Zhenodarov)
Answer: 5. Solution: Consider a moment when the rating has decreased by 1. Suppose that before this, $n$ people had voted, and the rating was an integer $x$. This means the sum of the scores was $n x$. Let the next viewer give a score of $y$. Then the sum of the scores becomes $n x + y = (n + 1)(x - 1)$, from which we get $y = x - n - 1$. The maximum possible value of $x$ is 10, and the minimum possible value of $n$ is 1; therefore, the maximum value of $y$ (on the first such step) is 8. With each subsequent step, the value of $x$ decreases by 1, and the value of $n$ increases by 1. Thus, on the second step, the value of $y$ does not exceed 6, on the third step - 4, and so on. Since any rating is not less than 0, the number of steps does not exceed 5.

It remains to show that five steps are possible. Suppose the rating at moment $T$ is 10 (with one voter), then the second viewer gives 8 points, the third - 6, the fourth - 4, the fifth - 2, and the sixth - 0. Then the rating sequentially takes the values $9, 8, 7, 6$, and 5.