Puzzle: digit $x$ appears $y$ times on this piece of paper.... There are ten questions on a piece of paper. Your task is to fill in each blank with a positive integer less than 10 such that there is no contradiction. You can reuse any digit.
The question is as follows:


*

*Digit 0 appears __ times on this paper.

*Digit 1 appears __ times on this paper.

*Digit 2 appears __ times on this paper.

*Digit 3 appears __ times on this paper.

*Digit 4 appears __ times on this paper.

*Digit 5 appears __ times on this paper.

*Digit 6 appears __ times on this paper.

*Digit 7 appears __ times on this paper.

*Digit 8 appears __ times on this paper.

*Digit 9 appears __ times on this paper.


How to solve it?
Edit 1:
I am not sure this question can be done without computer.

0 appears 1 time
1 appears 11 times
2 appears 2 times
3 appears 1 time
4 appears 1 time
5 appears 1 time
6 appears 1 time
7 appears 1 time
8 appears 1 time
9 appears 1 time
