Question 111
A sequence of integers is written on an infinite tape. The first number is $1$; each number except the first one is obtained by adding to the previous number its minimal nonzero digit (in decimal representation). Find the number of digits in the decimal representation of the number at $9 \cdot 1000^{1000}$th place in this sequence.
(I. Bogdanov)
(I. Bogdanov)