Normal sudoku rules apply. Digits an equal distance from the centre of a purple line must sum to the digit in the centre of that purple line. A clue outside the grid indicates the total of any digits in its row/column that neighbour at least one consecutive digit within that row/column. Eg, if a column, reading downwards, contains the digits 128396547, the clue at the top of the column would be 18; the sum of 1, 2, 4, 5, and 6, which are the only digits which neighbour a consecutive digit within that sequence. Cells separated by the black dot contain digits with a 1:2 ratio ie one digit is double the other.