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Fillomino (Futoshiki) (1023)
Instruction:
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 an area, including a value not present in the starting grid, such as 6 in a puzzle with only clues numbered 1-5.)
Place a number into each cell representing the area of the polyomino that cell is in. Each number from 1 to X must appear at least once in each row and column, and numbers greater than X may not appear in the grid. It is up to you to determine the correct value of X. Some inequality relations are given between adjacent cells; they must apply to the numbers in those cells.