The rules of this puzzle are simple. Cells can be in one of three states:

An UNSHADED (white) cell means that you have not considered this cell yet.
A DARK GREY SHADED cell means that the sum of the dark grey shaded cells in that row and column must equal the number in that cell.
A LIGHT GREY SHADED cell means that the sum of the dark grey shaded cells in all the connected cells must equal the number in that cell.