Normal sudoku rules apply. One cell in each row, column and box is a “doubler cell”. Doubler cells have a value equal to twice their digit. Each digit from 1 to 9 appears once in the set of doubler cells. Each grey line can be divided into one or more consecutive, non-overlapping sections each of which contains values summing to ten. Digits in a cage do not repeat. Values in a cage sum to the total in the upper left corner of the cage. Values on a black dot are in a 1:2 ratio (ie one value is double the other).