Normal sudoku rules apply. Exactly one cell in each row, column, and box is a "doubler", and doubler cells contain a complete set of the digits 1-9. A cell's value is equal to its digit, except that a doubler cell may or may not have a value equal to its digit multiplied by two. The same cell may have different values for the purpose of different clues. The sum of the values inside each cage is shown. The sum of the values along an arrow is equal to the value in the connected circle. Box borders divide each blue line into segments with the same sum of values. Along a green line, values differ from their neighbors by at least 5. A purple line contains a non-repeating set of consecutive values in any order. Values in cells separated by a black dot have a 1:2 ratio.