Normal sudoku rules apply: fill every row, column, and 3×3 box with 1–9.
Cages sum to the small clue in their top-left corner; digits cannot repeat in a cage.
A black dot joins cells in a 2:1 ratio; a white dot joins consecutive digits. Not every dot is given — an unmarked pair may still be consecutive or in ratio.
Cells joined by a V sum to 5; cells joined by an X sum to 10. Not every clue is given — an unmarked pair may still sum to 5 or 10.