Problem 43676. Count the Digits in the Box

In this problem you must provide an accurate census of all the digits inside a given box. The problem is complicated by the fact that your census report also appears inside the box, thereby influencing the result. Here is the simplest form of the problem.

 ----------------------------------------------
 |  The number of 0's inside the box is: ___  |
 |  The number of 1's inside the box is: ___  |
 |  The number of 2's inside the box is: ___  |
 |  The number of 3's inside the box is: ___  |
 |  The number of 4's inside the box is: ___  |
 |  The number of 5's inside the box is: ___  |
 |  The number of 6's inside the box is: ___  |
 |  The number of 7's inside the box is: ___  |
 |  The number of 8's inside the box is: ___  |
 |  The number of 9's inside the box is: ___  |
 ----------------------------------------------

Suppose you start to fill it in like this: there's only one 2, so you put a 1 next to the 2. But there are now two 1's, so you put a 2 next to the 1. But now there are three 2's... and so on. This problem eventually converges and can be answered as follows.

 --------------------------------------------
 | The number of 0's inside the box is:   1 |
 | The number of 1's inside the box is:   7 |
 | The number of 2's inside the box is:   3 |
 | The number of 3's inside the box is:   2 |
 | The number of 4's inside the box is:   1 |
 | The number of 5's inside the box is:   1 |
 | The number of 6's inside the box is:   1 |
 | The number of 7's inside the box is:   2 |
 | The number of 8's inside the box is:   1 |
 | The number of 9's inside the box is:   1 |
 --------------------------------------------

Count the numbers and you'll see the sums all work out. We will complicate this problem by adding some extra numbers to the top of the box.

Example

If

 extras = 22222

then we can see by inspection that one solution is

 census = [1 7 7 2 1 1 1 3 1 1]

as shown below

 --------------------------------------------
 | Here are some extra numbers:       22222 |
 | The number of 0's inside the box is:   1 |
 | The number of 1's inside the box is:   7 |
 | The number of 2's inside the box is:   7 |
 | The number of 3's inside the box is:   2 |
 | The number of 4's inside the box is:   1 |
 | The number of 5's inside the box is:   1 |
 | The number of 6's inside the box is:   1 |
 | The number of 7's inside the box is:   3 |
 | The number of 8's inside the box is:   1 |
 | The number of 9's inside the box is:   1 |
 --------------------------------------------

In general, your answer might not be unique. We'll just test whether you meet the criteria.