Normal sudoku rules apply. All cells in the grid can be divided into two orthogonally connected regions with no 2x2 square entirely in either region. Each cage contains one cell that is not like the others, ie. one digit in each cage is in a different region than are all the others in that cage. The sum clue in a cage is the sum of the “others” in that cage, eg. if the cage sum is 3 and there are three cells in the cage, there is an unknown digit that is in the opposite region from the other two, which are a 1 and a 2. Digits do not repeat within cages. A black dot joins digits that are in a 1:2 ratio. A white dot joins consecutive digits.
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