I see no interest in the problem, so let me show why I think the solution is kind of interesting.
To estimate the average value, let’s look at the smallest value, at the top of the 1 column, 1+1, and the largest value 10+10 at the bottom of the 10 column, whose average is 22/2 = 11. We next go down the first column to 1+2 and up the last column to 10+9. Going down one column gives a number one larger, and going up the other column gives a number one smaller, so again we have an average of 11.
We can continue this way, moving down one column and up the other, until we simultaneously get to the bottom of the first column and the top of the second. Now what? We move to the right for the small number and to the left for the second. This again increases one number by 1 and decreases the other by 1, so the average is the same. Now we can again go up one column and down another, and keep going like this, moving horizontally when the top and bottom of the columns are reached.
We finally reach the bottom of the fifth column with value 5+10, and the top of the sixth column with 6+1, which still add to 22 and have an average of 11. Therefore the average of everything is 11, and the total must 11×100 = 1100.