Every gold circle contains a different digit. In any row or column, its circle indicates the number of distinct digits that appears in that row or column. Any of these digits can be repeated any number of times in order to fill the row / column. Eg: one particular row has a circle containing a 3, meaning that row only contains three distinct digits - a valid example would be 173777131. Entering a correct digit may clear fog somewhere in the grid. No guessing is necessary. Along a lavender line, digits that are the same distance from the central spot sum to the digit on that central spot. Adjacent digits along a green line have a difference of at least 5. If a red dot sits between two digits, one is odd and the other is even. If a black dot sits between two digits, one is double the other.