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Fillomino Checkerboard (554)
Instruction:
Solve the Fillomino puzzle, with the extra constraint that it must be possible to color each polyomino region either all black or all white, so that black regions never share an edge and white regions never share an edge.
Fillomino Rules: Divide the grid along the dotted lines into regions (called polyominoes) so that no two polyominoes with the same area share an edge. Inside some cells are numbers; each number must equal the area of the polyomino it belongs to. A polyomino may contain zero, one, or more of the given numbers. (It is possible to have a “hidden” polyomino: a polyomino without any of the given numbers. “Hidden” polyominoes may have any area, including a value not present in the starting grid, such as a 6 in a puzzle with only clues numbered 1-5.)