Normal sudoku rules apply. Along modular lines, every set of three contiguous digits has three different remainders when divided by 3. Numbers outside the grid give the sum of the first X digits (the "X-Sum") along that row or column, where X is the first digit seen from the direction of the clue. In addition to any modular lines revealed as the fog lifts, every X-sum forms a hidden straight modular line at least X cells long starting from the cell closest to the clue. Digits separated by a black dot are in a 1:2 ratio. ALL blacks dots are given. As correct digits are placed, fog will lift, potentially revealing more clues.