This puzzle is solvable. Here is a hint.
Start with the right side. The 23 blocks allow you to find several black points in the rightmost column and the one next to it and the fourth from the right. This allows you to blacken more squares because of the 7, 8 and 9 in the rows.
And here comes the trick: In the 9th column from the right the biggest number is 6. That means that at least one of the incomplete 8 blocks cannot end in that row and must end in the rightmost one. And because there is only one block in the rightmost column, it allows you to cross out the square in bottom right corner.
This then allows you to find one black square on the bottom row because of the 17 block. because its a 1 in the column, cross out the square right above it. That allows you to fill in the 16 block in the row 2nd from the bottom. The rest of the puzzle is easy.
So do you still claim this is impossible to solve?
Because I have solved it and I didnt need to guess to do so.