6. (10 points) There is a magical tree with 63 fruits. On the first day, 1 fruit will fall from the tree. Starting from the second day, the number of fruits that fall each day is 1 more than the previous day. However, if the number of fruits on the tree is less than the number that should fall on a certain day, then on that day it will start over by dropping 1 fruit and continue according to the original rule, and so on. So, on the $\qquad$th day, all the fruits on the tree will have fallen.
【Solution】Solution: The total number of fruits that fall in the first ten days is:
$$
1+2+3+4+5+6+7+8+9+10=55 \text { (fruits) }
$$

There are still $63-55=8$ (fruits) remaining.
Then it starts over, with 1 fruit on the first day, 2 fruits on the second day, and 3 fruits on the third day,
$$
1+2+3=6,
$$

There are still $8-6=2$ remaining, which is less than the number of days, so it starts over,
Then 1 fruit on the first day, and then it starts over again, 1 fruit on the first day,
So: $10+3+2=15$ (days)
The answer is: 15.