What?-tenburg

Normal sudoku rules apply. Digits in a cage sum to the clue in the top left. Ambiguous Battenburg: Mark each cell of the grid with one of two different colours (e.g. red and blue) such that each digit always appears in cells of the same colour. (For example, if a 1 is in a red cell, all 1s in the grid have to be in red cells.) In any killer cage, all cells have the same colour (i.e. any cage is entirely red or entirely blue, but does not consist of both red and blue cells). Whenever 2 digits of both colours form a 2x2 checkerboard pattern, a Battenburg marking is given. If there is no such marking, the above pattern is not allowed.