So, let's begin.

Paint By numbers Tutorial. Step 1.

Look for a lines containing large numbers.
In this example, the largest number is 9 at the 4th and 5th rows and the row length is equal to this number so we can fill the whole rows.
Also, the largest number is 6 at the 3rd column so we can fill this column. Click on the solved numbers to cross them out. This helps you to keep track of your work.

Paint By numbers Tutorial. Step 2.

Look at the lines containing numbers, which is larger than (line length)/2.
In this example, one of such lines is the 1st row. You must place 7 contiguous solid blocks somewhere in these 9 blocks.
So, there can be two cases, when the solid blocks are placed at the ends of the line (left/right).
Note the middle 5 blocks are filled in both cases. This is the overlapping part. You can make sure of these blocks will be always filled in all other cases.

Paint By numbers Tutorial. Step 3.

Since 5 solid blocks are determined, it can help to determine some other blocks.
Look at the columns containing these solid blocks. You see the 5th column has been solved, so you can cross it out.

Also, it's easy to see that the 2nd and 3rd blocks at the 6th column should be filled.
At the 4th and 7th columns the black blocks correspond to [1,3], and [1,3]. These blocks should have length of 1. Therefore, there should be blank blocks on the bottom of these blocks. So, when a block is determined to be blank, place a dot as reminder. Also, click on the numbers that have been solved to cross them out.

Paint By numbers Tutorial. Step 4.

The number at 9th column are greater than (column length)/2, so you can fill the 2nd and 3rd blocks in this column.

Look at the rows containing these 2 blocks. It's easy to see what some numbers at the 2nd and 3rd rows have been solved, so you can cross them out([2,1,1], [3,1,1]).
Also you can place some dots at these rows.

Next, look at the 2nd row. Let's think about the left number. Since the 4th block is already solved as blank and the 3rd block is filled, you can fill the 2nd block. So, this row is solved. Don't forget to cross the left number in this row out.

Paint By numbers Tutorial. Step 5.

Now you see that the 3rd block at the 2nd column should be filled, and the column becomes solved, therefore the 1st and 6th blocks at the 2nd column should be blank.

Look at the top row. Since the 2nd block is solved as blank, it''s easy to see that the 2 blocks at the end of this row should be filled. You can cross this row out.
Also the right column becomes solved and you can cross it out.