Normal sudoku rules apply. Cells separated by a white dot contain consecutive digits. Not all white dots are given. The grey line is a "Double Digit Thermometer" where it alternatives tens digits and units digits. Starting at the bulb the double digits increase along the thermometer. All double digits added together sum to 400. Digits along each purple line multiply to 400. [NB Some people have questioned whether r3c2 should be counted twice in doing the multiplication. It should NOT be. It only counts once.]