Normal sudoku rules apply. Correctly placed digits clear the fog around them. The grid contains exactly fifteen cages that do not overlap and each cage occupies two or more cells. Digits cannot repeat within a cage. Not all cage sums are given but sums that are given are located in the left-most cell in the highest row reached by the cage. Two cages of the same size cannot have the same sum (regardless of whether either cage's sum is given). Digits in cells with a shaded circle must be odd. Digits in cells separated by a black dot have a 1:2 ratio.